OK, here's my point of view.
If this guy is just shy and does like you, yes, you putting the first move out there may be helpful. It might be the answer he was hoping for, so he doesn't have to muster up the courage to do it himself.
If he rejects it, it can still mean he's interested but maybe he's scared now. Or it could be that he's just not interested in that kind of relationship.
The "accidental" brush.. ohh, personally I love this one. It kind of makes the mind go wild, "did she mean to touch me there? Was what an accident? Does she want me to___? (fill in the blank)" and if he is interested it might be enough to get him aroused... which is nice because then you can really
see if he's interested or not.
Now, I don't know how old you are, but I'm guessing you're in your teens... This may be something that would work better for adults, I'm not sure, but you can also try to be direct. Tell him you like him and that you would like to go out with him. Ask him if he feels the same way. This may again ease his anxiety by not having to be the one to bring it up.
Just my thoughts...
