I think to understand. I too often wait to be 'invited' before joining a conversation, because I've fear that they actually don't want me. Sometimes even with friends. I think that it could be related to self-esteem.
A thing that helps me remembering that my friends do want me in the group is to fix in my mind at least an example of an episode in which they spontaneously asked me to do something together, or somehow shew pleasure to have me in the group/ in the conversation. So, when I think 'probably they don't want that I join' I can try to think to those moments.
This method isn't always enough, and it can't work with people that you don't know...but maybe it can help you a bit I hope so.