Keep Her Engaged
Once you've captured her attention (which is the most difficult part, so, congrats!) try your best to keep it. The best way to do this is by centering the conversation around her. She's not an egomaniac, she just wants to know you're genuinely interested. And, like in a job interview, the best way to do this is by asking purposeful questions. A woman discerns a lot about a man based on what he's interested in knowing about her.
On your end, keep the conversation light and interesting. The worst thing you can do when talking to a woman for the first time in a bar is reveal anything too intimate about yourself. Save that for your first date. Scratch that, your third.