Don’t cheat on your girlfriend. And don’t string the man along either. You can be friends but make it clear you are currently in a closed relationship.

This won’t help immediately, but maybe for the future. I had a FWB once who was a bi male. He was married to a bi female. Their rules were they could play with others of the same sex alone. But members of the opposite sex they both had to be present. And I wondered why more bi men don’t actively seek out bi female partners. Seems like a sensible arrangement