This also depends on how much wall space is in common between the bedroom and other parts of the house. In a previous house I lived in, the door was at the top

This also depends on how much wall space is in common between the bedroom and other parts of the house. In a previous house I lived in, the door was at the top of the stairs, and you would need a ladder / scaffolding to get to the part of the wall that was facing the stairwell. In that case there would be fairly little wall to reinforce with extra studs. Basically, wall studs are 16 inches apart on center (so a 14.5 inch gap between studs), so you would at most have to double the number of studs to have a somewhat less vulnerable room. Or, if retrofitting, several 3/4 inch plywood sheets screwed onto the vulnerable wall section, with decorative paneling covering them, may also be somewhat effective. Also remember that the object is to buy time. And most threats wont be a tactical threat, but from a random break in from someone that doesn't know much of what they are doing (but will know enough to panic shoot an occupant when they see one).