How to open up

I’m a very closed off person and tend to take a lot of time to open up and become comfortable with someone I’m with. I’m struggling to open up my emotional aspect of myself with my boyfriend of a month. I feel like that’s distancing him and making him question whether he wants to be with me. I’m a super chill person when it comes to relationships and don’t really rely on someone but I feel as though it’s a bad trait. He’s been bringing up how chill I am and I just don’t know if he’s hinting at he wants more out of me or not. How do I try and get myself to open up more or try and become a little more emotionally connected? Like what kind of conversation should I try bringing up I guess I don’t really know.