I have an account on bitbucket.org that I created by signing up with my Google account. Now everytime I log in I just click \"Log in with Google\" and that\'s fine.
How
You can attach a "proper" Bitbucket account password to your account. Go to https://id.atlassian.com/manage/change-password (sign in using your Google account) and then enter a new password in both the old and new password boxes. Now you can use your email address and this new password to access your account on the command line.
Note: App passwords are the official way of doing this (per @Christian Tingino's answer), but IMO they don't work very nicely. No way of changing the password, and they are big unwieldly things to type into the command line.