An exercise, which could be more advance is to first approach and then just say something. If you can't come up with anything, then just say hi.
The whole idea is to approach without having a script behind you and appearing canned. Doing so forces you brain to come up with ideas faster and being more spontaneous. Using your natural energetic physiology, something will pop up.
Rather than staring at her for a bit and then coming up with thing and then approach. Approach first, then say whatever pops into your brain.