You are conflating events.

Jefferson left Washington DC in March 1809 after Madison’s inauguration. He arrived at Monticello on March 15, 1809. https://monticello-www.s3.amazonaws.com/files/old/inline-pdfs/2009sRetireSmr09.pdf.

The DC schools started using the Lancaster method which included Bible reading in 1812. Jefferson was long gone by that time.

Webster doesn’t have anything to do with the DC schools. The Webster quote is dubious and doesn’t have anything to do with this post. /2013/01/09/david-barton-uses-jefferson-quote-he-says-is-unconfirmed/.

Edit to add: There is good reason to doubt Webster’s account of this quote. He said he visited Jefferson in June and they had delightful weather. A contemporaneous account of their visit to Monticello places Webster at Monticello in December with bad weather. Webster also needed to leave early due to receiving word that one of his children was ill. Webster didn’t write about this until 27 years after it allegedly happened. /2016/06/07/in-new-book-eric-metaxas-takes-a-page-from-david-barton/.

Since Jefferson was on the school board if he didn’t want the Bible used in schools he could have opposed it. A quote from Webster’s letter: “Raikes,” said Mr. Jefferson, “has done more for our country than the present generation will acknowledge; perhaps when I am cold he will obtain his reward; I hope so, earnestly hope so; I am considered by many, Mr. Webster, to have little religion, but now is not the time to correct errors of this sort. I have always said, and always will say, that the studious perusal of the sacred volume will make better citizens, better fathers, and better husbands…. https://books.google.com/books?

From letter 656

id=5Cx3AAAAMAAJ&pg=PA656&lpg=PA656&dq=%22Raikes,%22+said+Mr.+Jefferson,+%22has+done+more+for+our+country+than+the+present+generation+will+acknowledge;+perhaps+when+I+am+cold+he+will+obtain+his+reward;+I+hope+so,+earnestly+hope+so;+I+am+considered+by+many,+Mr.+Webster,+to+have+little+religion,+but+now+is+not+the+time+to+correct+errors+of+this+sort.+I+have+always+said,+and+always+will+say,+that+the+studious+perusal+of+the+sacred+volume+will+make+better+citizens,+better+fathers,+and+better+husbands.&source=bl&ots=vpJQfNpnVq&sig=ACfU3U1tQQYoR3oXmIBnC1EgftH-87gutA&hl=en&sa=X&ved=2ahUKEwjqjcCO-rDkAhUEna0KHSviA00Q6AEwBHoECAkQAQ#v=onepage&q&f=false

He was in Virginia when Webster visited him. The visit that Daniel Webster refers to in his letter. He went back to VA in 1810. They were still using the Bible after he left. Jefferson believed younger children (in their first 3 years of school shouldn’t receive lessons from the Bible)

I don’t see a reason not to use materials from any historical book but I don’t want my children taught from any religious book in public school. It isn’t just about forcing religion, it is teaching religion. Reading part of the primary sources to teach about the beliefs and their place in history seems reasonable. Teaching them the way Barton wants them taught is not.

It is likely that Jefferson never said that, at least in that way. In any case, it can’t be confirmed and even Barton said so (except when he wants to use the quote). /2013/01/09/david-barton-uses-jefferson-quote-he-says-is-unconfirmed/