I've dealt with the same problem when helping a friend to re-carpet a room.
It's dead easy:
Simply move all of the bedroom furniture clear from one wall by around 1.5m. Then cut a strip, roughly 1m wide off the carpet, roll it up and bin it. Then move the furniture a bit so that you can access the next 1m wide strip of carpet and cut it off. Repeat as necessary, removing the carpet strip-by-strip. (If required, remove the carpet grippers around the edge of the room whenever you find it convenient to do so during the step-by-step cutting-up process).
You'll obviously end up with a strip of bare boards, free from the clutter of any furniture, where you removed the final strip of carpet. So that's where you start laying your new carpet TILES (which are a zillion times easier to lay than full-size carpets). That's your solution!
;-)