Git keeps asking password for Bitbucket

The first reason can be that you have not set ssh keys. To do so, follow these steps. But step 4.9 for linux is not complete enough: you should expect ssh to tell you that the host is unknown etc. you can proceed safely.

The second reason can be caused on a per project basis, and it is because of the way you add your remote: you need to add it in the ssh format, not the https, like so:

git@bitbucket.org:myusername/myrepo.git

That's it.