Take it easy on the compliments.
While it's true every woman enjoys a good compliment every now and then, if you're layering them on thick, she'll think you're either desperate or insincere.
Also, if she's attractive, she probably knows she is. You're likely the fifth guy at the bar that night who has told her she's beautiful. Instead of adding to the verbal pile up, think of something original to say. Don't just focus on her looks. Give her an offbeat compliment like, "You order a martini like you've done this before," or "You have a firm handshake. Most women give the worst handshakes."
The key is not being nonchalant, but positioning yourself as someone with something new and different to offer versus the other schmucks that have approached her.