See Groovy site installation instructions
With git installed, you can checkout the bundle from github.
cd into bundle dir and clone the bundle:
cd ~/Library/Application\ Support/TextMate/Bundles/
git clone https://github.com/textmate/groovy.tmbundle.git
Now restart TextMate or tell it to reload bundles.
osascript -e 'tell app "TextMate" to reload bundles'
Now you're ready to go.
To update your groovy bundle, cd into the groovy bundle dir and run git pull origin master