Greasing Palms and Glad-Handing In Spite of Crippling Anxiety
Try a a little script for the introduction. Ask them two questions. Keep it simple: What do you think of this band? Or have you ever seen this DJ before? Then ask them something like "What are you working on right now?" or something similarly solicitous. Nod, smile a little and be interested in their reply. You do not need to bring up why you wanted to meet them or what exactly you want from them right then, but if the opportunity arises where that makes sense--go for it. It can be as simple as "I'd love to get you this new track I just finished." Aim to talk to them for three or four minutes, smile, say it was nice to meet them and excuse yourself to get back to your friend/get to the bar/make a call/buy some merch before the bands run out.
In order ot not be crushed by a fear of what-if, make a list detailing what is the absolute worst outcome that could happen. And then make an itemized list of everything that would have to transpire to get to the worst possible thing. In this case, you'd mortally offend them, they never talk to you or book you and get you 86'd from the scene by badmouthing you. Like, pretend that is even a possibility. What would have to happen? Short of telling some batshit racist anecdote, confessing to some sordid crime or similar act, coming out as a closet Nazi--I mean, how could that even come to pass? Nevertheless, make the list and it will take you out of the hamster wheel of your anxiety. It will give you traction out of the hole. I promise.
More real life style, lets say you are just awkward, shy-ish, say something weird and tangential and they think you are a weirdo? Then when you walk away they turn to their friend and go "What a weirdo," and maybe they gossip about you for 90 seconds? Realistically, unless you drop to your knee and do your best Jolson, people are not going to make too much of your interaction. Even if you do your worst, it's not a big deal. Resist the temptation to obsess on it, forgive yourself and do not apologize to anyone post-facto. Because it's not a big deal to be kind of bad at talking to people.
The thing about anxiety is that it can run riot and really distort one's thinking. Given how considerate you are in this letter, you are obviously a far cry from the assholes most people in the music biz deal with daily; you have that going for you.
Lastly, as long as your anxiety isn't isolating you from the world, you are doing pretty well. You have some good things going for you--I think it might even be a good idea to play it up a little. Everyone loves an enigma. Think MF Doom, ODB, Kool Keith, Captain Murphy. Awkward + curious backstory + rapping = golden. Maybe throw a cape and dish gloves in the mix? Dude, just think--you could become the Jandek of Bay Area rap. Let who you are work for you!