First, I've never said that bisexuality doesn't exist. Certainly I've met quite a few men and women over the years who, for one reason or another, become sexually and romantically involved with members of both sexes. The only thing I've pointed out is that this doesn't necessarily add up to true bisexuality in many cases. For instance, if a man gets married to a woman because he can't deal with his homosexual feelings, but he is mostly or exclusively attracted [if he's honest with himself] to men, is he is bisexual or a homosexual living a straight lie/life? Some people would classify any gay man who's had any interaction with a woman whatsoever, no matter how fleeting, as a bisexual, while others feel as I do, that a man can have interactions with women -- sometimes many and long-lasting interactions -- while being essentially homosexual. It can sometimes just be a question of semantics.
Notice I'm talking about gay/bi men. I have never pretended to be an expert in female sexuality, but I'll give your question a stab in any case. [First I'll just say in regards to the boyfriend you mention that there is a difference in loving someone and being in love with them with an all-consuming passion. Many men can feign a romantic and passionate interest in a woman -- almost as though they feel if they pretend hard enough it will come true -- while still being essentially homosexual. Not saying that's the case with the fellow you mention, but it does happen. Many homosexual men with wives truly do love their wives -- but more as "bffs" than as lovers they feel strong sexual passion and romantic attachment towards.]You mention games. I have to tell you that people, especially during the dating stages, do seem to play games [a lot of this is simply that people develop feelings for one another while still being uncertain if a particular person is "the one"] and it happens among both women and men regardless of their sexual orientation. It may be that you simply haven't met the "right" woman or that it's just too soon for you to feel entirely comfortable at the thought of a relationship with someone of your own sex. Someone can be very open-minded and liberal intellectually on the subject of same-sex relationships, and still feel a bit queasy inside when it comes to their actuality.
Don't sweat it. If you are honestly attracted to both men and women, don't worry about preferences for now. Keep the door and your mind open to any and all possibilities. Lesbians/bi women don't "play games" any more than straight/bi -- or gay -- men [or women] do. Once you recognize deep down in your heart -- whatever you may think you feel now -- that a same-sex relationship is as genuine and valid as any other kind, you'll be open to exploring this option in a positive and rewarding manner.
Best of luck!