Am bisexual, but the whole 'aren't bisexuals allowed friends then?' bit has been done so I'll leave that.
But can you sustain friendships with people you're attracted to? Good grief of course you can. I tend to fancy any friend I make in the early stages of the friendship, I guess it's me sending the feelers out to figure out if this is a potential romantic relationship or not. Most of the time I decide actually, I'm not into them like that, and I never think about them in that way again.
Sometimes I fall terribly in love with them. And as painful as it is if they don't feel the same way, from my experience so far, our friendship is actually more likely to survive if it's unrequited, because eventually I will move on and it will be water under the bridge, without the kind of mess you get with a break-up. The first person I was ever in love with - and I was crazy about her for a good couple of years - is still one of my best friends, almost ten years later. And I feel nothing romantic (or even sexual, although I still appreciate she's quite pretty) towards her any more.
It's a bit of a weirder kind of thing with my current boyfriend; we were close friends for years before we started dating but I had a boyfriend. We both fancied each other. We both knew we fancied each other. We both knew (well, really thought at the time) we were never gonna hook up. Nevertheless, we had a solid and uncomplicated relationship because, yehknow, there are much more awesome things that come with friendship than the possibility of sex.
He also has several female friends that I know he's fancied at some point or other in his life and this is why I don't mind. If I could think he was hot and hang out alone with him in his bedroom with absolutely no desire to cheat on my boyfriend at the time then I'm pretty sure he can exercise the same kind of self restraint.