Is there rating formula like ELO but for bughouse chess?
Providing that teams are not fixed, Elo (and Glicko too) does not fit your needs, because it's designed for 1-on-1 matches only.
You need something that manages both team performance and players' rating, as TrueSkill or rankade, our free-to-use rating system. Here's a comparison between aforementioned ranking systems.
Yes, you take the same formula and do absolutely the same calculations. Elo formula has very little to do with chess (except of it is used to calculate rating in chess). You can take any event that has win/lose/draw and apply elo formula to calculate the rating.
In bughouse you play in a team of two, so you will end up with a rating for a team.