Airplanes would work on me, but for women, try sketching something a little less....awesome.
If I had the skills to portrait, I would pull an attractive woman aside and sketch her like those 2 min artists do. Then work your magic from there. A funny cartoon version has the potential to go both ways, so I would stick with realism. Say you pulled her aside because you wanted to caputure her beauty, or some other attraction based thing. Tie in fate or opportunity, or some other key words to tie in a coincidence that you acted upon, its romantic and shows you have confidence. The discussion afterwards is critical. If she finds a connection, she will be more likely to call.
Glad your getting some face time. Now step it up.