How to encrypt data in bitbucket without losing git diff tools?

I used your attempt for some try-and-error and found a solution for your git-remote-gcrypt error. See my question Setting up an encrypted git repository.

You simply need to run

gpg --gen-key

which starts a dialogue to create a gpg key that can later be used for pushing to bitbucket. Compare the gpg manual

How to manage your keys

       This section explains the main commands for key management

       --gen-key
              Generate a new key pair using the current  default  parameters.   This  is  the
              standard command to create a new key.

              There  is also a feature which allows you to create keys in batch mode. See the
              the manual section ``Unattended key generation'' on how to use this.

Though, I don't know about further usage yet.

edit

I just tried to clone that repository onto another machine. Obviously one needs the gpg-key (and secret-key, whose name is implying that this is a bad idea) for that, so I decided to simply copy mine to the other machine. Sadly it does not work this way, such that we probably need to add other users.