Will they eventually leave you when the realize what they actually want? It's just a question of preference, some prefer sweet, some prefer savoury, some like it hot, some prefer cold, some like men, some like women, some like both. Just because they're attracted to both sexes doesn't mean they want both at the same time. The first step in establishing a serious relationship with a man who believes or is discovering that he is bisexual is to discuss what he means by the term. If you don't feel reassured and safe, it may be a relationship that needs to end.
You should ask your boyfriend if he feels he has got his bisexual adolescence out of his system.
I'm a bisexual girl with a great boyfriend... and a bunch of guilt
While there always are people who are going to be mean and intolerant, being more open about who they were brought them more support and friends than staying in the closet had. I hear you saying you really like and care for your boyfriend, but also aren't wanting a romantic relationship with him anymore, or at least right now. You nabbed them in the first place, so you are good as you are. Read Cruise Control by Robert Weiss. Whomever you date next, whether it's a girl or even another guy, I would recommend taking a break from dating and relationships for awhile to accept the end of your current relationship. If your motivations for dating a bisexual are just for some sexual fantasy, then be up front about it with your potential partner before the relationship develops. If he or she is a cheater, they're a cheater regardless of their sexuality.