I've known that I swung both ways since I was 16, and it's never been a big deal for me, although I've usually been quite discreet about it, and I've only had a few same-sex couplings. My last relationship ended, however, when I told my then-DP that I felt was attracted to men as well as women- this seemed to freak her out, and she ended things not long after, saying she wasn't comfortable going out with a bisexual- I think she may have misinterpreted that I was asking for permission to 'play around'- which I wasn't and wouldn't do in a monogamous relationship anyway.
Fast-forward 2 years and I'm now in a relationship with a woman who I care for deeply and with whom I can see things developing. She has some trust issues though (her previous 2 boyfriends both cheated on her, and the last gaslighted her to cover it up), and she wants us both to be completely honest with one another about everything. And I really want to be open with her and tell her about the way I am, not because I want to play around, but just so she knows who I am, but I'm worried that it'll put her off as well, because she might also be worried that it's part of me she can't satisfy (when it doesn't matter)