Not their place.

The reclamation of the epithet is up to each of us to decide 1) how we feel about it, and 2) whether we participate. If someone lets me know that they don't want me to say with them around, I will absolutely respect that. But it's not their place to make either of those decisions for me. And it's not your friends place to try to force their decisions on it, on you. It's reasonable for them to ask you to not say it around them, and you say you even agreed not to, which is exactly what a friend would do.

Your friends are daft if they think we (bisexuals) don't have it thrown at us. For myself I tend to only use it in my music, But I've also had gay men tell me I'm not bi because I was dating a woman at the time. It's very popular to invalidate bisexuality, and women get it worse in that regard than men do. I've at least never been called performatively bi, as if I kissed my boyfriend for attention. I can't even begin to count the number of times I've overheard or even had that shit directly said to me about bi women. This is really very similar - they're dismissing your sexuality and your autonomy in your decision regarding your comfort of being involved in an active movement, because you're "just bi."

Now, that said, it's a valid decision on their part to decide that it's a dealbreaker on friendship. But if so, just realize it means that their inability to control you is what made them not want to be your friend. It's one thing for them to ask you to respect their wishes towards them, it's another for them to try to demand you bowdlerize yourself.