Hello Katy
Personally, I think that, after knowing him for two years ~ even if not very well ~ and after being friendly enough to smile & wave, it really is time to talk to him.
I know you are shy, & perhaps he is shy, too, but I think that you could find something of mutual interest to discuss, if you tried.
What sort of music does he like?
Does he enjoy going to the cinema?
Does he like sports?
What are his ambitions?
What are his hobbies?
Just ask him some questions next time you bump into him, and be ready to tell him what interests you share and which of his interests you would like to know more about.
You don't say how old you are and where you see him.
If you work together or near each other, you could suggest continuing your discussion over coffee.
If you are at school or college, you could meet at lunch or in the library.
Just be friendly and keep it low key at first ~ then see how it goes.
Good luck!