To clone a git repository from BitBucket you can do that either via HTTPS (port 443) or via ssh which is port 22.
So your administrator may have to allow outgoing connections to port 22. https/443 are probably allowed already.
To open port 22 on Ubuntu run this command
ufw allow out 22
repo url should look like this git@bitbucket.org:your-workspace/project.git
If you really need to open 443 run this command.
ufw allow out 443
repo url should look like this https://your-username@bitbucket.org/your-workspace/project.git
If you need to deploy via ssh you need to set the private key like this. You need to add your public key in the repo
https://bitbucket.org/your-workspace/project/admin/access-keys/
export GIT_SSH_COMMAND="ssh -T -v -i $HOME/.ssh/bitbucket_deployment_private_key -o UserKnownHostsFile=/dev/null -o StrictHostKeyChecking=no"
If you need to generate private and public keys use qSandbox Bitbucket Deployment Key Generator
UFW commands are related to Ubuntu firewall commands and must be run as root.