Yep, this is exactly what I do. Though I will start collaborating on a private project beginning June and I am not sure how Bitbucket fares in that regard? Any experience with that?
I'm collaborating on some projects on Bitbucket and it has pretty much everything you need. It doesn't have some of the nice little touches that Github has like autocomplete emoji etc, but nothing that wouldn't make me miss Github if I had to move over to it 100% for private repos.