[obligatory "this'll get buried"]

Here's some unsolicited advice, but I guess being "bat at making friends" bothers you. I find myself in the same situation, but this helps a ton.

If you want to make real friends, the best thing you can do is to give a shit! Remember people's names and stories. Among the people with whom you can be friendly, identify those you find interesting. Learn about their hobbies, or whatever it is you find interesting, and get them to tell you about it. Make it less about them (which really is your perception of them) and make it more about what they care about, which to them, is more authentic, and more about them.

It's the difference between "gee, this person seems cool, and they are also into x-y-z, which I find interesting", and "gee, this person is passionate about x-y-z, I like that, I want to know more about that". I'm not saying neglect the person, but friendships develop through shared experience. Get them to share what matters to them.

It's easy enough to ask someone how they are, joke around, and get a couple of laughs. It's a skill you can learn, and for some, it comes quite easily. To develop connections, however, takes commitment and energy. And just because it's easy to be friendly with someone, if you find nothing interesting about them, there's no sense trying to pursue a friendship with them.

tl;dr: Figure out what that person is passionate about that you also have an interest in, and get them going on that.