dazzled, you could be me - although I don't think my colleagues are laughing at me behind my back, and if they are, they have the sense to keep it behind my back rather than come out with it in front of me.
I just don't know any single people at the moment. I'm early 40s, and in the last decade, everyone was busy coupling up and having children, and I just wasn't (quite happy to consider it, just no one else seems to want to consider it with me.) I do still see people from time to time, but I've had to accept that I have to be the one who has to fit in round them, because they have no choice but to consider their children in any plans - either a child-friendly time and place, or they have to sort out babysitters, or I have to go to their house. It's just not possible to phone someone and say, "fancy a pint?" on the spur of the moment after a bad day.
I do do evening classes and exercise classes, and a few other things, like some voluntary work, and I meet acquaintances through all that, and have even been out for a pint (to discuss some plans for an event), but none of it's developed into a real friendship, and I got through things like my parents' deaths with not a lot of support, as everyone was up to their ears in nappies.
I did make sure part of my holiday last year was a group activity (yoga week), so I didn't spend my entire time alone, but also, it wasn't the entire holiday, so that if I didn't get on with the people, it wouldn't wreck the whole time (as it was, they were mostly great.) However, as I'm not used to spending so much time with people, I was also quite glad to get back to having some time for just me. I may spend too much time on my own, but I'm also used to it, and it means I also need a certain amount of time alone (just probably not quite as much as I get.) I do do quite a few things by myself at weekends - trips to London galleries, or in the summer, down to the beach and so on, because otherwise, as you say, you wouldn't do anything at all. But there are things I tend not to do because I'm on my own, and there are things I would prefer to do with someone else, but it's not always possible. I do make an effort to see if people will be about if I am going to be in their area of the country, and will maybe take an extra day so I can meet up with them, but it's a local social circle I need to develop. Not holding any more parties, though, after only three people came to the last one a few years ago - I do tend to do things on a one to one or one to small group basis these days.
I would think if you work full-time, and you're doing a masters, the amount of spare time you have is fairly limited anyway (I don't remember having much spare time at all when I did my masters.) The thing that would really bother me is people feeling they have the right to comment on it and tell me how to live my life. If I decide I want to meet someone, I will ask for help, but if I'm not asking, I don't want it unsolicited, because there's not actually an obligation to be in a relationship. I don't necessarily want or have time for a full relationship - I would just like a bit more of a social life in general, mostly the sitting round in a group and just chatting about nothing in particular. And if other people feel they need to comment on it, they can either make sure I get invited along to things, or they can sod off.