I sided with the Brotherhood of Steel and got Danse to stay alive after the Blind Betrayal quest. However every time I go to see him at Listening Post Bravo (where he hides out) it won't let me fully talk to him. I want to travel with him again but every time I try to talk to him all he says is "hi" and walks away. Is there a quest or something I have to do before continuing my travels with Danse?
I fear that you may be experiencing a bug. The wiki has two bugs that I believe it to be.
Consoles and Pc:
If completing the main quest line, Danse can become bugged to where the Sole Survivor can no longer initiate dialog with him (thus unable to do his quests) despite being friendly with the BOS.
There is also another bug that seems to be for PC only. I don't know what platform you are on since you did not tag it or mention it. The bug reads:
Danse may bug where one can no longer talk to him, even if the Sole Survivor hasn't completed the main storyline. If he does, one will no longer be able to finish any quest where the player character have to talk to him. The only thing that seems to solve this problem is to reload a save from before ever having any contact with him.
Try reloading a save before this happens. You will unfortunately lose any progress made up to this point, but it may resolve your issue. You may even have to go back before you met him defending the police station, but I would first try a save that's more recent.