You can enable SSH for Git access at the system settings page. A hostname and a port number which are used for SSH access are required.

Also, you have to set the base url of your GitBucket instance to enable SSH access. Note that if you have a reverse proxy and it has a different hostname from the GitBucket server, a hostname in the base url is different from a hostname for SSH.

Then, repository url for SSH becomes available.

Users who want to use SSH for Git access have to register their SSH keys to GitBucket.
First, create a key using ssh-keygen:
$ ssh-keygen -t rsa -b 4096 -C "your_email@example.com"
id_rsa and id_rsa.pub are generated in ~/.ssh. Then, register the content of id_rsa.pub at the account settings of GitBucket:

That's all. SSH access is now available.