How should I (23M) go about asking out this girl (22? F)? If anyone here has experience with South Asian girls, please offer advice

So basically I am a 23 yo male who has never had a serious girlfriend. I'm not a bad-looking guy at all, but my entire life I have suffered extreme shyness and anxiety around attractive women which has prevented me from ever lasting more than two weeks in a relationship. Also, although I am a white guy, I absolutely love Indian/Pakistani girls, whom I consider to be the most beautiful women on the planet.

I am currently in university, and because my school is located in my hometown, I still live with my parents. I generally take the subway back home every afternoon and occasionally I stop by the local supermarket. One time (about two weeks ago), I dropped by to get some energy drinks and found an absolutely gorgeous Indian girl at the cashier. I was the only customer at that particular till and she was quite obviously flirting with me throughout the exchange. I should have asked for her number right then and there, but I didn't.

Since that time, I have started going to the supermarket more often, always buying 2-4 items as a pretext to hopefully catch this girl on her shift. I have seen her there three times since, but have not yet had the opportunity to ask her out. On the other hand, she has not been particularly flirtatious during any of these encounters but this could be because each time there were other customers present, many of them older people (50+, or even seniors), so I'm thinking she might not have considered it appropriate.

This afternoon was going to be the day that I finally asked her out, so I walked into the store as usual, trying to keep my composure, although my heart was racing, selected the same energy drink and walked up to her till. Unfortunately, however, there was quite a long line-up, so a DIFFERENT girl, also South Asian, who did not have any customers offered to help me instead, and not knowing what to do, I said "OK."

Now, here's the dilemma. This girl was very pretty as well and she seemed to be smiling, so I reasoned that there was a chance she might like me as well, but with the other girl standing at the other till I decided not to ask her out. As I was making my purchase the girl looked at me from the other till, and I felt genuinely embarassed so it was all I could do to look down. Now I fear that she will see me as a complete wimp, p***y, etc. and that I have ruined any chance I have with her, so I need some advice on what to do. Should I wait a few days before going there again or should I keep trying every day until the opportunity arises? If I do come too often, will I risk coming off as a creep? Or should I just drop the first girl and take my chances with Girl #2 (20? F)? Also, does anyone here have any experience with Indian women and how they approach dating, and if you do, how does that factor into the approach I should take?

TL;DR; 23M shy, inexperienced. I like a cute Indian girl at the local supermarket (22?F), but have not taken my chances and feel that I have made things too awkward. There is also another girl at the same store whom I find relatively cute and I'm thinking maybe I should take my chances with her instead. Any advice would be greatly appreciated.