Phone number or other contact info. Supposing you’re on good terms, they’re not someone you’re interested in romantically or the like (so none of the anxiety from that at least), what’s kept you from asking?
Supposing that something has on occasion, anyway.
This was an issue for me when I was watching my then toddler son a lot as a father.
We would meet other parent-child combinations regularly at the places where you go with children. Most of the time it would be mothers.
But even though the settings were obviously non romantic and child focused, it often was difficult to get into a friendly relationship. I always had the impression the mothers were careful to not do anything I might interpret as flirting, including talking. So the interactions were limited to the now and then on the playground. No getting-to-know conversations.
Remarkably that was much simpler with the same women when the fathers were around also, I.e. on weekends.
In short it was a long series of strange encounters and isolation. It’s much simpler to interact with women without their children around, regardless if romantically motivated or just as factual interaction.
During the whole parenting time of 3 years I had with that child I made one(!) contact that I could message things like “wanna meet up in this or that interaction?” My wife has 15 or so.
Absolutely this!
As a dad, I was always extremely cautious when I was out with my kids talking to moms out with their kids. I also talk about the now, because I’m not trying to confuse anybody.
One of the more uncomfortable moments: my kid was playing and interacting with a child & parent. I said hello. She immediately took her kid and left the play area.
Another time: I must have been talking to a single mom because she kept asking me to be her 3 yo’s male role model multiple times.
I gave up trying to make friends with other parents at playground areas since then.