dnd 5e – What bonus would be balanced against restricting a changeling’s Shapechanger trait to only work once per day during a long rest?

I think the answer by TheDragonOfFlame is a fair assessment and I also recommend going with the Actor feat without the +1 to Charisma if you are going to go with that option. What I would more strongly recommend is talking with your DM about why he is restricting what is literally the defining characteristic of your race of choice.

If he is afraid of your character abusing the ability, ask him to clarify how he thinks you might do that. I can definitely see the occasional edge case where you might do so, but I doubt it would make much difference to typical play. In fact, I would argue that it would create opportunities for your character to do some fun espionage work.

It might be worth mentioning to him that changing your appearance is only one part of a disguise, and barring some magical means, costume changes can be quite difficult to pull off on the fly. There is also acting the part and sometimes pulling off appropriate dialog or having to know some password or even a trivial fact about who you are impersonating can prove to be fatal to this kind of subterfuge. Remind him that your success at these things is not automatic (though, as a bard you will certainly have advantages to such things).

Most of all, try and come to an understanding between both of you that makes you both happy. Make sure you’re wanting to play/run the same kind of game and if something is off, find a compromise. Even a few sessions in, you’re better off adjusting things to have fun than slogging through something you don’t enjoy.