Git doesn't prompt for password and fails with similar cryptic message "fatal: protocol error: bad line length character: user" if you don't have your private key authentication setup as well.
https://www.digitalocean.com/community/tutorials/how-to-configure-ssh-key-based-authentication-on-a-linux-server tells how to specify public key on the server. Basically add the public key to ~/.ssh/authorized_keys or ~/.ssh/authorized_keys2
I had to struggle a bit on how to provide private key to the Git Bash on the windows machine. Dan McClain's answer in https://serverfault.com/questions/194567/how-do-i-tell-git-for-windows-where-to-find-my-private-rsa-key/382801#382801 describes that. One addition to his answer, in my case the private key file was expected to be named id_rsa.pub