Socializing exposure

I think your mistake is assuming that you will find someone to exchange numbers with every time you decide to talk to someone. You have no way of knowing who is single, who is attached, what they like, etc. So why not just start with the goal of talking to someone without exchanging numbers first?

As a girl, I am simultaneously flattered and scared when a guy approaches me 🤣 my thought process: "There's a lot of people out there with bad intentions, or just suck as people, so why spend the energy just to find that out? And potentially risk my safety?" So, ya know, I end up in a self-defeating pattern 🙃 The way I would want to be approached is a "non-beauty"-based compliment, e.g. compliment my shirt that is about a specific interest (Sonic the hedgehog, for example lol), "those jeans rock" is much more comfortable than "you look good in those jeans." Personally, I will politely say thank you regardless and try to move on with my activity. If someone asked me a relevant question after that or shared a relevant tidbit, THAT is my window to choose to engage or not: if I say something to carry on the conversation or give a curt answer and re-busy myself. If someone doesn't engage, it's for a thousand other reasons than YOU not being good enough. I've definitely been approached by people that I would want to engage with but I was tired, my brain is mired in something that happened at work, I had a first date last week that did NOT go well and I'm not ready to even try, I'm in a hurry, I'm buying something that is odd or particular and I don't want someone to judge, etc.

I'm sorry to hear you had this experience. Sometimes people at the grocery store are just trying to grab what they need and get on their way. What about socializing at a library? Ask a question about a book a person is carrying, or if they are in the same section you are in, ask for a book recommendation. People are usually interested in striking up a conversation if it is something they are reading or a topic they are interested in. Please don't be discouraged about your initial attempt. Anxiety can be so rough to work through, but you will find your way.