Is it okay for you to take initiative in asking him out? Absolutely it is okay. I am sure it would have been nice if he asked you first, but it isn't like there is some law saying the guy HAS TO ask first. As a ridiculously shy guy myself, I can confirm that him NOT asking you out does not necessarily mean he is not interested. In fact, I can't know this for sure, but based on what you've described my guy reaction would be that there was at least some interest on his part.
Again, not like I can know that for sure. To be perfectly honest, I think given the situation you describe, my advice would be to just go for it. Being 22 and 33 is not such a big difference. Just as an example, it is much different from being, say, 18 and 29. That's the exact same numerical difference (11 years), but yet very different in practice. At 18 you are still very young, still very much a kid even though you are legally an adult (in the US anyway, not sure the age in other countries). But you really aren't an adult yet. So 18 and 29 are maybe not so compatible (generally, anyway) but 22 and 33 could be.
So, with the age difference covered.... it sounds like you two are no longer in a professor/student capacity. Unless the new university you will be attending happens to be where he works. If so, then maybe it would be best to wait. But, if not then you are now officially not professor/student, you are just two people. So, no reason for awkwardness or any concern of impropriety there.
But, honestly, the most important reason why I personally think you should just go for it.... If you don't there will be part of you just left wondering "what if?" Possibly forever. Even if you ask him out only to be rejected.... at least you know. Sure, it would suck, but at least then you know and can move on. But... what if you ask and he happily accepts? Wouldn't you be kicking yourself for even considering not trying? Does he like you? We can't know that for sure any more than you can. It certainly sounds like there is at least some interest on his end. Maybe he had reasons for not asking, or maybe he truly was just too shy. Believe me, I know from experience that us shy guys can want to ask a girl out VERY badly and yet still never do it. Unless he suddenly decides to ask you out, the only way you'd ever know is if you take the initiative first. So, I say go for it!
Best of luck to you.