Here's my 2-cents. I think the foundation of any relationship is trust and understanding. If someone is closeted about part of their sex life during the serious stages of a relationship, I would find it harder to understand why they didn't trust me enough to tell me. Serious relationships should have a bond that transcends normal stereotypes and typical lack of understanding. After a set time you know whether or not you can trust your partner, be it straight, bi, or gay.
I've only had relationships with women, and one bi-woman. I know that, as a man, it's nice to automatically assume that we leap at any sexual impulse, and bi-guys are seen as "double the pleasure, double the fun".
However, bisexual is a measure of sexuality. It breaks down into two setups, bisexual preference and bisexual intimacy. Most people have bisexual tendencies (Kinsey and other studies confirm this) and the fact that some people are honest and have acted on them does not make them less of a lover.
The question is, do you care for the person or the choices they make. Sometimes, people do unsavory things, but that doesn't mean the entire person is bad. If you were to date someone that was bi, and they did not tell you until after you were married, it shouldn't have an impact--because they may still be bi, but they are with you.
Sexuality is not a switch, or a choice. It's how you are made. However, like all things in life, there are choices on actions, not on evolution. You can choose to be heterosexual with gay tendencies or homosexual with straight tendencies, or just plain equal opportunity. The thing to remember is, if you are bi and dating a member of the opposite sex, that person turns you on and you are connected to that person. Therefore, that person is your intimate partner. This does not mean that at the first sight of the same sex, the bi partner will go running drooling.
I can't tell you the number of other married straight buddies of mine that will see a woman and comment, "Yea, I'd f* her". That's not much different than a bi individual commenting about the same or opposite sex, the only difference is the gender of the target. The person making the comment is choosing to not act on their "desires" and their sexuality is independent of their willpower to say no to impulse.
I think it's similar, in a way, to couples where one partner has a fetish that the other does not understand. If you have a partner that is into S&M, but you are not, and you still have a vibrant sex life, then it's a matter of understanding "it's not their thing."
I think it's important to consider that if the person has put the effort into developing a "serious relationship" with you, then clearly they are interested in you. Their sexual orientation is oriented towards you and only you. Sure there will be temptation. There is always temptation--regardless of sexuality. Trust your partner and be happy.
