The Doctor's Bag should work. But in my experience, you need a 100% (minimum 90%) Doctor skill in order for it to work every time. Lower than that and you may fail 2 out of 3 times. It's a pretty demanding skill.
Hmmm I'll try again but I'm pretty sure my medic squad member has 101% doctor and when I try to use it it just says "Does Nothing."
EDIT: Yep, did nothing. Maybe there's a patch I need because when I traveled around the wastes the Bandaged condition stayed. Bugs are so annoying.