It depends a lot on the individual. If you think you would benefit from having your own room, book your own room. Its asinine to put a grand or so in one time potential savings at the top of the list of considerations at the beginning and most important part of a multi million dollar career.

I put buying your own newspaper right up there with lighting cigars with $100 bills. I'm as cheap as the next pilot and understand we're wired that way. The month or so you spend in initial training is NOT the time to focus on petty savings. No one is that amount of money away from liquidating. If you benefit from your own hotel room, get the room.