I am no expert with obsolete notes by any means, but for what it's
worth, even if this is a counterfeit note, which I am not sure that
it is. It would still be worth something to someone.
The age alone, if it can be documented to be authentic, would make
the note a nice find.
Bank of America then was not what it is today, it was ABNco "American Bank note Company", a company owned by the government to print paper money for many different banks and for the US. I have only been able to find one such note with the same B of A across the front from New York, but it was printed much later and was deemed a counterfeit note. The value was still around $195 in Fine+ condition.
Find someone who knows about obsoletes, perhaps a show in your area, and bring the note for an estimate and authorization. You might be surprised at what you find out?
Good luck, I think it is a real find no matter what.