I agree with Leed that a text or email would be the way to go.

As you don't seem to see him regularly I don't think it'll come across as cold. The very fact of sending it will tell him you're thinking about him and you're interested in him.

I'd personally just keep the first one short and vague and see how he replies. If he's interested, you'll know. You could then lead on to asking him out on a date if you wanted but that would open the door to the possibility of outright rejection so I'd perhaps only do that if he responds and shows some interest back. Shy people can be completely different in writing so you may see a different side of him.

I think also the key is to remember that asking someone out that you like and have known a while is a completely normal thing. And it's the only way to know as by the sounds of it he isn't going to approach you.

I guess the only downside is he may not reply at all so you'd have to factor that in as a possibility but it seems unlikely. More likely than that, he will reply and you'll get an idea how he feels.