Does it matter whether a bedroom door swings in or out of the room?
There is no code that tells you that your bedroom doors need to swing in for a bedroom.   But it is usually not a good idea for them to swing out.


as you mentioned the doors present an obstruction in spaces.  In hallways it might even be comical to wind your way around 7 open doors from both sides.  
when you are talking about privacy the doors have swung in because of the hinge side would be protected.  For instance if you locked your door and the hinges were out someone could just knock the pegs out of the hinges and release your door.
and safety wise there is always a chance that someone will open a door on someone else.  But not many people stand next to the door in their own room.  But people could be passing by where ever and you could hit them.  This should be thought about in your case.
aesthetically speaking you will be showing the hinges on the outside.  I know it isn't a huge thing but a small design factor.


I have to say I have finished maybe close to 50 basements now (got to be close) and one of my favorite designs for a smaller basement is simply storage room with the bathroom towards the front and the other side is huge living room with an "extra" room with french doors in the back.  Extra room is big enough to house a pool table but could easily be converted into a bedroom (often we have a walk-in closet going from extra room to storage room).  We usually have the French doors swing out to the living room.  If the living room is small though we swing them in.  This is highly dependent on what you feel is going to be next to the French doors on each side of the room. (On really small rooms we use double pocket doors)

Another note:  Come to think of it the doors themselves play a big part of inside or outside.  If I have some nice doors - especially the wooden vintage french doors we clean up - well these open out.  Because we want to showcase the door.  If it is some big box generic french door set, we hide them in the room.