Like other posters have said, I would ignore those saying that this realisation means that you will cheat, or that you can't have just suddenly turned that way or this is all about just having sex etc. There are so many factors that go into sexuality (and for me sexuality is not just about the physical act, but is a fundamental part of who we are) and for some people finding out who they truly are can take years to come to the surface.
I am in my early forties and have finally acknowledged last year that I am bisexual. I remember being about 11 and thinking about kissing my best friend, but I was brought up in a deeply religious environment and even at that young age was taught that if you were gay you were going to hell, so I apologised to God and rationlised that my brain got mixed up as she was such a good friend. When I finally left the church I got married very soon afterwards to a man that came from a culture that did not approve of being gay. Although he was okay with meeting people in gay relationships, he often voiced his disapproval or disbelief that people could want to be physically or emotionally with a person of the same sex. So all of those factors have gone into me burying, for years, who I am.
I am still married to that same man, however he has become a lot more relaxed over the years and accepts that people are gay and that they should have a choice in who they love. The thing is, I could never say to him who I am, I know him and I would know this would be the end of my marriage. I have told my mother and sister (gay and bisexual themselves) and a couple of good friends, so I have a decent support network if I need it.
Like tornadoalley said up thread, this comes with a lot of difficult choices, however it is not one I think you should rush into. For me this means giving myself a lot of time to think and also throwing myself into various activities for a bit of distraction. I do a lot of exercise, spend time with my children and immerse myself in work. My marriage is not all that great - there are a lot of issues there, but I feel it could be salvagable as the children get older and for them I have decided to work on it. I also think I am heading into perimenopause, and that is honestly playing havoc with how emotional I am, so I have decided to give that a chance to settle down before I make any decisions.
For me personally, I am going to really just knit this into the fabric of who I am, grieve for the fact that I may never explore this side of me and try and find other things that I can focus my attention on. When I spoke to my mum about this she told me to be careful that I was not doing the grass is greener scenario and for her being in a relationship with a woman could be just as hard sometimes as being in a relationship with a man. I can't predict what will happen in the future though, the urge to be emotionally and physically with a woman can sometimes feel overwhelming, but I take each day at a time.
Give yourself time and be careful who you tell (or you may get responses like some of those in this thread) - but most of all be compassionate towards yourself, we can't help how we feel or change who we are.