I understand the impulse.
Grocery stores, book stores, libraries, classrooms, airports, and planes. I am a little more stimulated than normal in all those kinds of places. I have engaged with women in the past in these places, always mindful that my banter might not be welcome, and observant to whether it was being genuinely reciprocated.
Though I preferred to play the 'long game' in grocery stores. People are regulars at grocery stores, so you do not have to rush things.
I would try and time a check out with a pretty girl so I could be chivalrous and let her cut. Then engage in some playful small talk. At that point, I would do nothing, though I would make a point to remember something about the conversation. If I saw the girl in the store again, I would approach and ask her abut the thing I remembered, which would usually take their memory back to the initial meeting. At this point I might ask their name. But nothing beyond that. From this point though I would consider them a 'grocery store friend' and talk to them when I saw them.
From this point, I would wait for a 'change' or an 'event'. If they had a change in appearance I could compliment them on, or if the shopping was before a holiday event like the 4th of July or the Super Bowl or something where I could ask them about their plans in a non-prying way, and extend an invitation of some kind. Generally they would have plans that close to the event. At which point I would reply 'Some other time perhaps' and then pay very close attention. If they greet that enthusiastically, I would make another invitation on the spot. Sometimes I would even be responded to with an alternative invitation.
When you do get out with ladies through this process, the sexual tension is super crazy on the date, because the odds are you have both been thinking about it for quite a while.