ssh-keygen -t rsa -C "youremail@gmail.com"
cat ~/.ssh/id_rsa.pub

Copy public key into SSH keys on BitBucket
ssh -T git@bitbucket.org (to verify)
vim ~/.ssh/config

Add:

Host bitbucket.org
     IdentityFile ~/.ssh/id_rsa

and save.

git clone git@bitbucket.org:username/project-file.git
(to the project file)

git pull (should now work without auth)

Create a file git.php in the theme directory with the contents:

<?php `git reset --hard HEAD`; ?>
<?php `git pull`; ?>
<?php `find . -type d -print0 | xargs -0 chmod 0755`; ?>
<?php `find . -type f -print0 | xargs -0 chmod 0644`; ?>

Go into project settings >> hooks and add a new POST hook directed at the git.php file. For example:

http://yoursite.com/wp-content/themes/yourtheme/git.php