alt Hacker NewsI can vouch for this with my experience.
Back in grad school, I was out making new friends. I was playing tennis 4-5 times a week. I'd invite players for post-game coffees (in the morning) and dinner (evenings) at every game. Consistency mattered. I'd ask every time. Slowly we had our regulars. Our coffee times became an institution in and of themselves.
People are busy, yes. But, people also want to be in demand. People also don't want to be rejected. And, people also don't want to be left out.
Asking around, I was exposing myself to rejection. Some folks appreciated their time being demanded. More still joined because they didn't want to be left out.
Tennis is a great hub for connection when you're retired. I play a lot, and people are always meeting up after we play and forging all sorts of non-tennis relationships. Sadly for me, this is all during the day when I'm rushing back to work hoping my 90m absence didn't coincide with some emergency.