When you use bitbucket with a google account, you have no password. One solution is to create a password with "app passwords". There are about 30 permissions, which subset is required for git (e.g. using Sourcetree)?
I would prefer to use SSH keys, but I cant add mine as its already added with another organisation. In theory its possible to have multiple SSH keys with bitbucket and Mac, but havent managed to get it working yet.