Only you can decide for yourself what is the right thing to do, but I think you need to tell all of this to your boyfriend. Especially the part that you would never act on these feelings without his permission. But, look, a relationship doesn't have to fit any standard mold. It should fit for you and your spouse, that's it.
If that means you have a threesome, that's OK.
If that means you never try sex with a girl, that's OK too, as long as you continue to be satisfied with that.
It could mean that you sometimes have sex with other people, or only women, without your boyfriend as long as he's OK with that.
It could mean that you have sex with women sometimes and he has sex with men sometimes, if he's interested in that.
It could mean that you have sex with women sometimes while your boyfriend watches and doesn't join in.
It could mean anything that you and he want it to mean. But you can't know what he might want unless you talk to him about it.
For myself and my husband, we're monogamous. I'm totally gay (no interest in girls whatsoever), and he's bisexual. He's satisfied not having sex with girls anymore. We've talked about having other sexual partners, but we decided that didn't work for us. I'd be OK with it, but he thought he might get jealous if I had sex with someone else. We've talked about having threesomes, and we both agree that could be fun, but we haven't met someone we both want to have sex with yet. If we do, we might do it. Right now, just having sex with each other is keeping us both satisfied.
My sister is bisexual, but she's never had sex with a girl, only guys. Her husband knows this. He's totally strait. As far as I know, they're monogamous, too. She says it doesn't bother her never having tried sex with girls, and neither one of them wants to try a threesome or other sexual partners.
I have a couple of friends who are married to each other (both men) who have an open relationship. They are free to have sex with whoever they want, pretty much whenever they want, as long as they are always truthful about it with each other. They have a lot of 'casual' sex where they don't even know the other guy's name. That works for them.
I don't know anyone personally, but I have heard of relationships where only one person has sex with others. This is usually in a 'cuckold' situation where the husband enjoys seeing his wife have sex with other men. As long as he's happy with that arrangement, that's OK, too. Or the wife might be bisexual and the husband enjoys watching his wife have sex with other women.
It only matters that you work out some arrangement that BOTH of you are happy with, and that you talk it over again whenever one of you feels UNHAPPY about the arrangement.
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You don't need to hide, my friend, for I am just like you.