There really is no specific definition as to what constitutes a bedroom, however, the industry standard under ANSI, HUD/FHA, FNMA, and most Lender guidelines is - the room must be finished and has to have heat, electricity, closet (with shelf - closet rod - door - and at least 7 linear feet), ingress/egress - meaning its own entrance/exit from a main area or hall and emergency exit such as a window (loacal building codes determine minimum window size and minimum height from floor to bottom window sill), primary bedroom must have at least 130 sqft excluding closet, secondary bedrooms must have at least 110 sqft excluding closet, must have a ceiling height of at least 7 feet except under beams, ducts, and other obstructions where the height may be 6 feet 4 inches. If a roomâ€™s ceiling is sloped, at least one-half of the finished square footage in that room must have a vertical ceiling height of at least 7 feet, however, no portion of the finished area that has a height of less than 5 feet may be included in finished square footage. And it is not considered a bedroom if one has to pass thru the room as the only access to another room, excluding master baths as the other room.
For appraisal purposes, in my opinion (your market area may react differently), it would be wiser to have a permanent wall. The increase in value, if any, would mostly depend on your market's reaction to differences between 3 and 4 bedroom homes and is generally determined by matched pair analysis.