Chill On The Unsolicited Compliments
Much like the guy unimaginative guy sending her drinks, burying her in compliments gives off the unmistakable scent of desperation. Are you not capable of starting a legitimate, human conversation? Why are you telling me I'm beautiful when you should be saying hello?
There's also the much-mentioned point that women who are attractive are used to being complimented and therefore do not want to hear about how hot they look. That's complete bullshit. Women live on a steady diet of compliments, and require being fed them often. Even if she looks like a cross between Paula Patton and Kate Upton, she'll never tire of hearing how her eyes sparkle when she smiles.
The distinguishing factors here are quantity, originality, and timing. One or two genuine compliments delivered at the right time is plenty. Try giving her a simple compliment mid-way through the conversation rather than at the beginning, like "I wanted to say this earlier, but you look amazing tonight." Somehow, it seems more genuine this way, and is much more effective.