SHY GUYS- He doesn't start the twitter convos, should I still give him my #?

[Hiiiii]

I want to get to know this really really shy guy but he doesn't talk a lot and we dont see each other much. He says hi/hey when we pass each other most of the time, smiles, sometimes waves. I direct message him on twitter and tweet to him and he replies like 4 times, acting engaged in the convo and then stops so idk ... I want to text him but... isn't the twitter thing of not always replying to dms kind of a bad sign? should I keep "chasing"? He might actually like me & is acting like this because he is, by nature, reallyyy quiet & shy. He doesn't often start the convo, but maybe he doesn't know what to say or have anything to say. But I really feel like I should have my turn being chased... Right? I haven't talked to him in a couple days/ maybe a week.

When we do have face to face conversations though, I have caught him like 3-4 times full-face blushing and it is the cutest thing ever. For no reason. We'd be talking about a band and he turns soo red. And it's not like he's embarassed in front of anyone because we would be in a room alone most of the time. So I think that is a green light, a good sign. Do you?

I just don't like starting the convo so much......
I feel like I'm being pushy but I'm probably overthinking... right?

SO, SHY GUYS,.........Do I go for him, be direct, & give him my #? Or wait for him to 'catch up' & actually put in more effort? Do you think he would text me?

[Tom]

Give him the number. He may not like putting his business on a social network, I'm not even that shy (kinda but not really) and I don't do it. And as to the not dm'ing you back, maybe he had nothing to say to what you said or found it uninteresting. (which is a totally different subject) but you get the point.