The bark peeled off like sheets of paper so I assumed it was paper Birch
most all birches have trees that can be very papery. trees found in different varieties can have tight bark also. I think the name "paper" could not be a very good way to distinguish species.
white birch in the eastern us looks rather different in bark color from yellow. and I think you are correct that it might be a better bow wood. white and paper can be chalky white and have whit branches also. yellow can tend towards copperey. leaves on the yellow are different ,too.
I use a sub variety of white birch, and it is hard to compare as a bow wood without having both on hand. I have compared notes with some bowyers from Finland and Sweden, and I am told european birch is considered to be inferior to the american, but again, it was not mentioned which one in america, and the same is often repeated here about birch as a bowwood being inferior, I just try to find the densest birch I can
The slower growing birch I have I collected from better drained soil in mountainous areas is better than what I find in the lowlands. Looking at the article in wikipedia, I see both birches growing in the eastern US in coal country, and only at higher elevations the further south you go with some good pics of each.