The "bedroom" issue is a matter of some debate among many involved in Real Estate. Lofts do not have doors on many of the rooms, but they do have closets and windows and are called bedrooms. Some clients install folding screens or sliding doors to close off the rooms and for privacy.
It is generally agreed that the room must have a closet to be considered a bedroom, othewise it is called a "den".
You may have your own ideas about what a "bedroom" is. In that case I would be very clear with your Realtor, and let them know what is acceptable to you and what is not. That way, you will not waste your time on unsuitable property, and your Realtor will be able to screen out homes that do not meet your criteria.
Gail Mercedes Cole
For example I have seen two bedroom homes with a large living room and large dining room around 2000 sq ft and I have seen four bedroom homes that were like cubes around 1300 sq ft. I personally would have chosen the larger home and brought in an architect how to redesign and make it work for my needs.
Hence I would not get focused on terminology. When that is important you can always pull the permits and then you will know what is "legal" and what is not.
Prudential California Realty
Beverly Hills, CA