He (Barton), has no evidence of a bible printed by congress because there is no such thing.
Barton never said Congress printed a Bible.
Congress has never had a printing press.

What Barton has always said was that the Aitken Bible was the only Bible to receive Congressional approval.
From The Manhattan Rare Book Company
Aitken Bible
"The Bible of the American Revolution":
First Edition of the Extraordinarily Scarce Aitken Bible,
The First American Bible, of Profound Importance in Defining the Freedom and Identity of America
The Aitken Bible: Rare 1782 First Edition
As long as the United States remained under British rule, the British government forbade the printing of Bibles in America. When the Colonies declared their independence, the importation of Bibles became restricted and by 1777 there was a severe shortage of Bibles in America. On September 11, 1777, this shortage of Bibles was brought to the attention of the Continental Congress by its chaplain, Dr. Patrick Allison. He said in his report that Bibles were urgently needed because, “the use of the Bible is so universal and its importance so great” and on Dr. Allison’s advice, Congress passed a resolution to make every attempt to import 20,000 Bibles in English “from Holland, Scotland, or elsewhere, into the different parts of the Union.” The importation of Bibles soon proved to be nearly impossible and the Continental Congress had to search for another alternative to supply the population with their most important book.
On January 21, 1781, the noted colonial printer Robert Aitken petitioned Congress for both sanction and support for the production of a complete Bible for the American people and a committee was immediately formed to determine if Aitken were qualified to produce a book of such significance. Aitken’s impressive credentials (he had, among other things, been the publisher of the Journals of Congress for the first Congress and published numerous articles by Thomas Paine) convinced the committee and on September 10, 1782, a Congressional Resolution was adopted granting Aitken permission and financial support for the printing of the first edition of the first American Bible.