LIMITED POWER OF ATTORNEY

Know all by these presents, that the undersigned hereby constitutes and appoints
each of John Dziewisz, Brittany Helmick, Ashley Colando, Amy Saus, and any duly
appointed Assistant Secretary of Babcock & Wilcox Enterprises, Inc. (the
"Company"), signing singly, the undersigned's true and lawful attorney-in-fact
to:

     (1)  prepare, execute in the undersigned's name and on the undersigned's
          behalf, and submit to the U.S. Securities and Exchange Commission (the
          SEC) a Form ID, including amendments thereto, and any other documents
          necessary or appropriate to obtain codes and passwords enabling the
          undersigned to make electronic filings with the SEC of reports
          required by Section 16(a) of the Securities Exchange Act of 1934 or
          any rule or regulation of the SEC;

     (2)  execute for and on behalf of the undersigned, in the undersigned's
          capacity as an officer and/or director of the Company, Forms 3, 4, and
          5 in accordance with Section 16(a) of the Securities Exchange Act of
          1934 and the rules thereunder;

     (3)  do and perform any and all acts for and on behalf of the undersigned
          which may be necessary or desirable to complete and execute any such
          Form 3, 4, or 5, complete and execute any amendment or amendments
          thereto, and timely file such form with the SEC and any stock exchange
          or similar authority; and

     (4)  take any other action of any type whatsoever in connection with the
          foregoing which, in the opinion of such attorneys-in-fact, may be of
          benefit to, in the best interest of, or legally required by, the
          undersigned, it being understood that the documents executed by such
          attorneys-in-fact on behalf of the undersigned pursuant to this Power
          of Attorney shall be in such form and shall contain such terms and
          conditions as such attorney-in-fact may approve in such attorney-in-
          fact's discretion.

The undersigned hereby grants to each such attorney-in-fact full power and
authority to do and perform any and every act and thing whatsoever requisite,
necessary, or proper to be done in the exercise of any of the rights and powers
herein granted, as fully to all intents and purposes as the undersigned might or
could do if personally present, with full power of substitution or revocation,
hereby ratifying and confirming all that such attorney-in-fact, or such
attorney-in-fact's substitute or substitutes, shall lawfully do or cause to be
done by virtue of this power of attorney and the rights and powers herein
granted.  The undersigned acknowledges that the foregoing attorneys-in-fact, in
serving in such capacity at the request of the undersigned, are not assuming,
nor is the Company assuming, any of the undersigned's responsibilities to comply
with Section 16 of the Securities Exchange Act of 1934.

This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, 4, and 5 with respect to the
undersigned's holdings of and transactions in securities issued by the Company,
unless earlier revoked by the undersigned in a signed writing delivered to the
foregoing attorneys-in-fact.

IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be
executed as of this fifth day of May, 2020.

                                  Signature:  /s/ Henry E. Bartoli

                                     Print Name:  Henry E. Bartoli