Take out the ax...time to chop this girl off her pedestal.
There have been times in my past when a girl was "perfect." It caused me to go a little too AFC and I was thinking way too much about her. However, if you take a step back, "see the forest from the trees" and see everything as they really are, you'll see she is not perfect. She could definitely be a great gal...just not perfect.
Earlier this school year, I met a girl in one of my classes who seemed to have it all - similar interests, personality, looks, head on her shoulders, etc. However, while I was in pursuit, it didn't take me long to realize this girl is not perfect. For starters, she was a closet attention wh*re. She wasn't blatant about it (as some girls are), but you could tell - just watch her when she's talking to other guys. Second, she was deathly scared of confrontation. She'd do anything to get out of a situation. She gave me a bs excuse about something once, I saw right through it, and I have never seen any girl leave so quickly. Finally, this goes along with the attention wh*re thing, she'd try playing all sorts of games. Instead of being herself, she'd sometimes start doing some strange things just to see what happens, and if any guys would cater to her or not.
In conclusion, there's a decent chance you're dealing with a great girl. Just realize she isn't perfect and you're probably just as good as her - if not better.
...). If she's not interested because you are solidly in the LJBF, she'll shoot you down but gently. If that happens, chalk it up to a learning experience and realize it was your fault and pull the trigger faster next time.