I don't think there is anything wrong with asking...and I would really have no problems asking someone, but, I prefer to send signals and let him ask, because I need a guy that can be somewhat assertive or aggressive.
I have sent pretty strong signals though, when I am interested!
In your situation, how often do you see this guy and interact with him? Me personally, I would talk to him a bit, decide if there was some interest, then open the door for him. The way I have opened doors before depends on the particular situation, and includes things like
at a party, I went up to my future H, took his hat off his head and stuck it on mine, and sat on his lap. He got my phone number and called me.
2nd H, I went over to his friend, told his friend I thought his friend (my future H) was cute, and he came over and asked for my phone number.
WS - a mutual friend came by to tell me he thought I was beautiful, so I told friend to have him come and talk to me. He did, got my number and asked me out.
One guy, I just smiled at him a lot. A lot. Flirty. And made eyes at him. He asked for my number.
One guy, we were talking, he seemed interested, so I worked into the conversation that my "EX husband" was this or that, but was sure to mention EX....he asked what types of things I liked to do, we went out.
And on again/off again SO, we talked and flirted a while, he asked me out, I actually stood him up
so a little while later, when I decided I DID want to go out with him, I told him he needed to take me dancing. He did.
I figure if I give the signal, if he doesn't pick up and run with it, he isn't going to be what I am looking for. But that is me. I doubt most people are looking for the same things I am, so if he seems a bit shy, and you like him, I think many guys are flattered when the girl asks them out, but I also think it is good to make an easy out....such as....Would you like to get coffee sometime? Then he can say yeah, sure, whatever, and you can say...."well, let me know when you have some time available." That way you leave it with him to decide if he really wants to, and he will pick it up and finish the arrangements if interested.