crossroad,
IMO its better to have shopped for the high efficiency speaker first, but here you are, so lets start by asking good questions:
1. How big is the room?
2. How far back will you be listening?
3. What kind of music will be played?
4. How loud will you be listening?
5. Are you willing/able to DIY?
6. Are you interested in used?
7. What is the design of the amp (SET, push-pull, etc.)?
When I think bedroom system, a smallish room, sitting on the bed, can't play too loud (late night, neighbors/family considerations) come to mind. So high spl's and deep bass are out, but higher efficiency with fairly tall driver placement would be in order. Throw in your $300 budget and you'll be hard pressed to get decent sound even going DIY or used.
For $300 plus shipping, assembly, and finishing (and using my assumptions above) you could get a very nice pair of Bob Brines FT-1600 Mk II:
http://www.geocities.com/rbrines1/Pages/FT-1600_MkII/Main.html