well, in a 1 and 2gb system i rather have 32 bit windows, and you cant have 32 bits Windows with a 64 bit UEFI... in any way, i do belive there are 64 bit BT systems around.
I thought that it was the other way around. You could load a 32-bit OS, with 64-bit UEFI (admittedly, I haven't tried this, but why would that make that incompatible, when 64-bit BIOS could load both 64-bit OSes and 32-bit OSes), but not the other way around, without some severe workarounds.
My N2830 laptops are BT-M, and they came with 4GB RAM, and 64-bit Windows 8.1 (w/Bing?).
Edit: Even on a 1-2GB system, I think I would personally prefer to run 64-bit OSes, to take advantage of 64-bit programs like Waterfox. Then again, that might be sluggish with 1GB RAM, I don't think 64-bit Windows really likes to run in 1GB of RAM. Maybe 2GB.