in the redesign of interactions that the dungeon court has brought, it seems XP bars were lost.
characters get exp passively by being assigned to rooms. i assume either they get a little bit of EXP per time passed, or they get a little bit on room production. i lean toward the latter as my characters assigned to slower producing rooms seem to stay lower levels.
characters gain exp when they kill another character in combat.
characters also gain exp when returning from a mission to the surface. they get more if they succeed in their task. i find this to be the most reliable, timely, and efficiant form of leveling characters.
combat is slow, sacrifices prisoners for corpses, and can only apply to one character at a time. passive room assignment exp is waaaaay too slow, even with all the positive traits that apply.