printers and their drivers are notorious for being intentionally unsupported as soon as possible. comes from generic ink and the failed distribution model of underpriced printers and overpriced ink, and the fact that comsumer printers reached the apex of their current technology 10 years ago.
either get your own printer, dual boot, or just run a 32bit os. Most apps and games are still 32bit dx9, and seeing it a laptop, for school, with the limitation by the school, i don't think you'll have any problem.
More than likely there are some printers that have 64bit drivers. The types of professional printers used atty schools don't go unsupported like cheapo consumer ones and 64bit windows OSes have been around since XP. I don't see anyway there wouldn't be 64bit drivers for some even if they can't be bothered.
A good brother laser mfc is a good investment though. Mines been going for 8 or 9 years. And works on 64bit. Worst case you can put you papers on a flash drive and print from a school computer or download an official 32 bit iso and install with your key if it's Big deal. Laptops don't really NEED more than 4GB of memory so no big deal. Or dual boot it