Should I keep in touch with him?

Hello, I'd like to ask you...
In December, I started seeing a guy who was helping me with a preparation for my entrance exam to university. I developed a feeling for him almost right away. He was always so kind, well-mannered, patient... He used to make me tea anytime I came, he complimented me, made me laugh etc.
Anyway, when I finally had the courage to admit my feelings, he was already taken. He tried to make me feel better about it, saying that he is flattered and that he enjoyed teaching me... Things like that.
The exams are over now and we already said goodbye to each other. But I still miss him a lot.
I considered writing an e-mail to him, but firstly: I don't really know what to write, and secondly: I wouldn't want to bother him. Moreover, him being in a relationship makes it even harder - I wouldn't want him to think that I'm desperately trying to "get him back" in any way. I know the girl he is with and she is also very friendly, always happy, has a nice smile and so I'm happy for them.
But I can't seem to overcome it. The fact that I probably won't see him ever again makes me sad. It's been like this for over three months now and there's no improvement.
What should I do? Should I write him or give it time? I was told that eventually, it will all go away.

Thank you for your answers, it means a lot!