How do I make a friend if the odds are against me?

This may sound crazy but I need some opinions.

I have this neighbor who seems really cool. He plays in a band (the drums) and they're great. I got to meet the band once and they were all very nice to me! When we talked C, (my neighbor) said he would come and introduce himself to my parents and I was like, cool, he could be a new friend!

But he never showed up. I was dissapointed, but it's okay.

The issue is though, I want to be his friend because he seems really cool, but there are several factors against me:

He's an adult, he's busy, and it probably seems really weird for me to try and say hi.

I've been considering just writing a little card to him for Christmas or whatever, because I wanted to thank him and the band for his music.

My mom thinks that's weird, she's probably gonna call it "innapropriate"or something and I don't want to get in any crap with her.

Any thoughts?