BSOD are almost never caused by games, they are caused by driver or hardware issues or failures. Googling the error code you get will help pinpoint it.
Skyrim will run on 8.1, but it's not supported (You won't be able to get official support from Bethesda beyond general advice), but there's plenty of forum goers here that have it running on Win 8.1 will be able to help.
I've found that disabling Steam Community in game also helps, if the game pushes you close to certain hardware limits.