<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>012 - Disclosure - Bank Credit Facility</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode /><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol /><contextRef><ContextID>Context_6ME__30-Jun-2013</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000086264</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2013-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2013-06-30T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS /><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels><Label Key="CalendarSupplement" Id="0" Label="6 Months Ended" /><Label Key="Calendar" Id="1" Label="Jun. 30, 2013" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>1</Level><ElementName>us-gaap_DebtDisclosureAbstract</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Bank Credit Facility [Abstract]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>us-gaap_DebtDisclosureTextBlock</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>verboseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="Context_6ME__30-Jun-2013" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div style="line-height: 11.4pt; text-indent: 0pt; display: block;"&gt;&lt;font style="display: inline; font-family: times new roman; font-size: 10pt; font-weight: bold;"&gt;&lt;font style="display: inline; text-decoration: underline;"&gt;Note 6 &amp;#8211; Bank Credit Facility&lt;/font&gt;&lt;/font&gt;&lt;/div&gt;
&lt;div style="line-height: 11.4pt; text-indent: 0pt; display: block;"&gt;&amp;#160;&lt;/div&gt;
&lt;div align="justify" style="line-height: 11.4pt; text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;"&gt;&lt;font style="display: inline; font-family: times new roman; font-size: 10pt;"&gt;Nytis LLC&amp;#8217;s credit facility with Bank of Oklahoma which matures in May 2017 has a borrowing base of $20.0 million and a maximum line of credit available under hedging arrangements of $9.5 million.&amp;#160;&amp;#160;Carbon and Nytis USA are guarantors of Nytis LLC&amp;#8217;s obligations under its credit facility.&lt;/font&gt;&lt;/div&gt;
&lt;div style="line-height: 11.4pt; text-indent: 0pt; display: block;"&gt;&amp;#160;&lt;/div&gt;
&lt;div align="justify" style="line-height: 11.4pt; text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;"&gt;&lt;font style="display: inline; font-family: times new roman; font-size: 10pt;"&gt;No repayments of principal are required until maturity, except to the extent that outstanding balances exceed the borrowing base then in effect; however, the Company has the right both to repay principal at any time and to reborrow.&amp;#160;&amp;#160;Subject to the agreement of the Company and the lender, the size of the credit facility may be increased up to $50.0&amp;#160;million.&amp;#160;&amp;#160;The borrowing base is redetermined semi-annually, and the available borrowing amount could be increased or decreased as a result of such redeterminations.&amp;#160;&amp;#160;Under certain circumstances the lender may request an interim redetermination.&amp;#160;&amp;#160;The facility has variable interest rates based upon the ratio of outstanding debt to the borrowing base.&amp;#160;&amp;#160;Interest rates are based on either an Alternate Base Rate or LIBOR.&amp;#160;&amp;#160;The portion of the loan based on an &amp;#8220;Alternate Base Rate&amp;#8221; is determined by the rate per annum equal to 1.5% plus the greatest of the following: (a) the Federal Funds Rate for such day plus one-half of one percentage point, (b) the Prime Rate for such day or (c) LIBOR for a one-month LIBOR Interest Period plus one percentage point.&amp;#160;&amp;#160;The portion based on LIBOR is determined by the rate per annum equal to LIBOR plus between 2.5% and 3.25% for each LIBOR tranche. For all debt outstanding regardless if the loan is based on the Alternative Base Rate or LIBOR, there is a minimum floor of 4.5% per annum. The credit facility includes a hedging component that provides a line of credit under commodity swap, exchange, collar, cap and fixed price agreements and agreements designated to protect the Company against changes in interest and currency exchange rates.&lt;/font&gt;&lt;/div&gt;
&lt;div style="line-height: 11.4pt; text-indent: 0pt; display: block;"&gt;&amp;#160;&lt;/div&gt;
&lt;div align="justify" style="line-height: 11.4pt; text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;"&gt;&lt;font style="display: inline; font-family: times new roman; font-size: 10pt;"&gt;At June 30, 2013, there were approximately $12.6 million in outstanding borrowings and approximately $7.4 million of additional borrowing capacity available under the credit facility.&amp;#160;&amp;#160;The Company&amp;#8217;s effective borrowing rate at June 30, 2013 was 4.77%.&amp;#160;&amp;#160;The credit facility is collateralized by substantially all of the Company&amp;#8217;s oil and gas assets.&amp;#160;&amp;#160;The credit facility includes terms that place limitations on certain types of activities and the payment of dividends, and requires satisfaction of a current ratio (the ratio of current assets (including borrowing base capacity) to current liabilities as defined) of 1.0 to 1.0 and a maximum funded debt ratio (the ratio of the outstanding balance of all interest bearing indebtedness to the sum of EBITDAX (net income plus interest expense, income taxes, depreciation, depletion, amortization, exploration and impairment expenses and other non-cash charges) for the most recently completed fiscal quarter times four) of 4.25 to 1.0 as of the end of any fiscal quarter.&lt;/font&gt;&lt;/div&gt;
&lt;div style="line-height: 11.4pt; text-indent: 0pt; display: block;"&gt;&amp;#160;&lt;/div&gt;
&lt;div align="justify" style="line-height: 11.4pt; text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;"&gt;&lt;font style="display: inline; font-family: times new roman; font-size: 10pt;"&gt;On June 28, 2013, the Company and Bank of Oklahoma amended the credit agreement whereby the Company&amp;#8217;s loans under the credit agreement will no longer be subject to a minimum interest rate floor of 4.5% per annum for LIBOR tranches commencing after July 25, 2013 and loan amounts subject to the Alternate Base Rate after July 31, 2013.&lt;/font&gt;&lt;/div&gt;
&lt;div align="justify" style="line-height: 11.4pt; text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;"&gt;&amp;#160;&lt;/div&gt;
&lt;div align="justify" style="line-height: 11.4pt; text-indent: 0pt; display: block; margin-left: 0pt; margin-right: 0pt;"&gt;&lt;font style="display: inline; font-family: times new roman; font-size: 10pt;"&gt;The Company is in compliance with all covenants associated with the credit agreement as of June 30, 2013.&lt;/font&gt;&lt;/div&gt;</NonNumbericText><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>nonnum:textBlockItemType</ElementDataType><SimpleDataType>na</SimpleDataType><ElementDefenition>The entire disclosure for information about short-term and long-term debt arrangements, which includes amounts of borrowings under each line of credit, note payable, commercial paper issue, bonds indenture, debenture issue, own-share lending arrangements and any other contractual agreement to repay funds, and about the underlying arrangements, rationale for a classification as long-term, including repayment terms, interest rates, collateral provided, restrictions on use of assets and activities, whether or not in compliance with debt covenants, and other matters important to users of the financial statements, such as the effects of refinancing and noncompliance with debt covenants.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 505

 -SubTopic 10

 -Section 50

 -Paragraph 3

 -URI http://asc.fasb.org/extlink&amp;oid=6928386&amp;loc=d3e21475-112644



Reference 2: http://www.xbrl.org/2003/role/presentationRef

 -Publisher SEC

 -Name Regulation S-X (SX)

 -Number 210

 -Section 02

 -Paragraph 19, 20, 22

 -Article 5



Reference 3: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 210

 -SubTopic 10

 -Section S99

 -Paragraph 1

 -Subparagraph (SX 210.5-02.19,20,22)

 -URI http://asc.fasb.org/extlink&amp;oid=6877327&amp;loc=d3e13212-122682



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