I am also around 60, I enjoy close relationships with a few current and/or former providers, and I chat, text, and talk with them regularly. I have "dated" and even enjoyed off the clock sex with a few, and I have combined social outings, especially sporting events, with BCD time with quite a few. I think one key is that I have been a good customer first, and built a friendship over several visits. Another key is that I have never demonstrated any jealousy, and have always tried to help them with their business in any way possible.
If you see a provider regularly and you feel like you have a good relationship and you enjoy each other's company, don't let your age be a barrier. There are numerous legitimate friendships between providers and hobbyists, and providers are probably more receptive than civvies to social relationships with older men. I mean, they have already gotten over the hard part, right? If they can manage to convince you that they enjoy sex with you, going for a nice dinner or a special event should be the easy part.
I will just add that I am not advocating stalking or pushing boundaries with respect to BCD time. If a woman likes you it should be obvious through her behavior. If you ask her to dinner after a session and she tells you she doesn't see clients off the clock, let it go and move on. As a direct answer to your question, though, yes, it does happen, and it even happens with older guys.
Oh yeah, one more thing... I have NEVER paid for social time.