While it makes total sense that you don't want to end things and hurt her (and potentially lose a close friend), I'm also not hearing reasons why you want to continue this as a romantic relationship. You feel like you're lying and I'm hearing a lot of guilt that you don't feel the same way for her that she feels for you. But that's nothing to feel guilty or bad about. You can care about someone deeply in a non-romantic way and still not want to date them. Too, staying in a relationship on the off chance you will grow to love someone is really just delaying the inevitable. Even if you really want to, love and attraction aren't things you can force yourself to feel. As painful as it as to consider, from what you're describing the kindest thing you can do for her and for you is to end this relationship. Does that make sense?
While being attracted to guys doesn't mean you can't also be attracted to girls, do I have it right that you haven't or don't experience attraction to women (either women you know or celebrities), including the person you're dating? Too, it may also help to read something like this article to see if any of identities described feel like a good fit to you: The Rainbow Connection: Orientation for Everyone
. Since you weren't interested in dating or romance before, can I ask why you eventually said "yes" to going out with your friend?
As an aside, while you may feel like you'll never have a close friend besides this person, odds are extremely good that you will. Even people with social anxiety can form close friendships with multiple people (I say this as someone with that trait), so if you do lose or change your relationship with your friend, it won't mean you're doomed to be forever alone.