Gale should tell his bedtime story to non-romanced characters (that he likes?) the night after the party, but this doesn’t give you any romance with him. From memory, it’s triggered entirely in conversation rather than by clicking on the bedroll.

So it sounds like a bug if he’s actually offering to spend the night rather than just tell a story the next day. Do you not get an option in your dialogue with him the night after to ask him to just go on and tell you?

"You may call it 'nonsense' if you like, but I've heard nonsense, compared with which that would be as sensible as a dictionary!"