Serves you right.
Why do you feel cheated? If anyone should feel that way she should. She was cheated out of having a good partner.. one she actually deserves.
You should feel cheated, dude. She mis-represented herself as being bisexual, something you were obviously looking for in a woman. If she's not, she's the one that lied, so kick her to the f*cking curb.
I'm sure if someone's bisexual it doesn't mean they always want to be in a 3some. Some people just like to be with multiple people some don't. Not all bisexuals do. She probably just likes girls and she likes guys (but got cheated out of a decent relationship when she wound up with someone like you) and was looking for ONE guy or girl to spend her life with. That's not weird.
I'm bisexual and the thought of a threesome makes me feel sick. I'm not prudish, I'm up for most sexual things, but a threesome is a complete turn off.