Building trust with s/o advice?

My bf has some trust issues and says I've done a few things to break his trust. I've never cheated or done anything to deliberately hurt or upset him. We've been together a little less than two months and I've tried to be as understanding as possible into letting him take his time with building his trust in me. But he doesn't like that I'm so "flirty" with everyone (girls and guys) or so open about things going on in our lives. Also doesn't like that I hang out with my ex, we dated over two years ago and are strictly friends who have both moved on but still he dislikes it. Says he doesn't want to change me but I'm aware some of my single habits may be destructive, and I want to adjust. I've agreed to be less flirtatious and to ask for permission to disclose what we defined as personal information if I want to talk about it, and in return he will attempt to be more open with me about himself. But it all feels very confining and I just want to know how do I build trust with him in a healthy manner? Is this agreement with him a good idea? Is adjusting my behaviour the same as changing myself and is it a good or bad thing? Advice please!