<?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>1040 - Disclosure - Bridge Financing</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>D2013Q2YTD</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001436304</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_WarrantsAndRightsNoteDisclosureAbstract</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>Bridge Financing</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>kyth_ClassOfWarrantOrRightDisclosureTextBlock</ElementName><ElementPrefix>kyth_</ElementPrefix><IsBaseElement>false</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>terseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="D2013Q2YTD" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div style="font-size:10.0pt;font-family:Times New Roman;"&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&lt;b&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt; FONT-WEIGHT: bold;" size="2"&gt;4. Bridge Financing&lt;/font&gt;&lt;/b&gt;&lt;/p&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;In connection with a Bridge financing in 2006, the Company issued warrants exercisable for approximately 243,000 shares of Series&amp;#160;B redeemable convertible preferred stock (&amp;#8220;Series&amp;#160;B Preferred&amp;#8221;) at an exercise price of $7.6055 per share.&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;Prior to the Company&amp;#8217;s initial public offering (&amp;#8220;IPO&amp;#8221;) in October&amp;#160;2012, the Company classified the warrants as a liability and re-measured the liability to estimated fair value at June&amp;#160;30, 2012 using the Black-Scholes option pricing model under the following assumptions: contractual life according to the remaining terms of the warrants, no dividend yield, risk-free interest rate of 0.17%, and volatility of 58%.&lt;/font&gt;&lt;/p&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&amp;#160;&lt;/p&gt;
&lt;p style="MARGIN: 0in 0in 0pt;"&gt;&lt;font style="FONT-FAMILY: Times New Roman; FONT-SIZE: 10pt;" size="2"&gt;The increase in the fair value of the warrants from issuance through our IPO in October&amp;#160;of 2012, totaled $1,205,000 and was recorded in warrant and other income (expense), net, and included $467,000 and $381,000 of interest expense in the statement of operations and comprehensive loss for the three and six months ended June&amp;#160;30, 2012, respectively. Effective immediately prior to the closing of the Company&amp;#8217;s IPO in October&amp;#160;of 2012, the warrants for convertible preferred stock became warrants for common stock and were reclassified to equity. All but 178 warrants were exercised during 2012, with the remaining warrants being exercised in January&amp;#160;2013, resulting in the net issuance of 153,000 shares of common stock.&lt;/font&gt;&lt;/p&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>Disclosure for warrants or rights issued, which includes the title of issue of securities called for by warrants and rights outstanding, the aggregate amount of securities called for by warrants and rights outstanding, the date from which the warrants or rights are exercisable and the price at which the warrants or rights are exercisable.</ElementDefenition><ElementReferences>No definition available.</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Bridge Financing</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>Bridge Financing</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>true</HasCustomUnits><IsEmbedReport>false</IsEmbedReport><IsMultiCurrency>false</IsMultiCurrency><ReportType>Sheet</ReportType><RoleURI>http://www.kytherabiopharma.com/role/DisclosureBridgeFinancing</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows></InstanceReport>
