To update to a new version of Ionic, open bower.json and change the version listed there.
For example, to update from version 1.0.0-beta.4 to 1.0.0-beta.5, open bower.json and change this:
"ionic": "driftyco/ionic-bower#1.0.0-beta.4"
To this:
"ionic": "driftyco/ionic-bower#1.0.0-beta.5"
After saving the update to bower.json file, run gulp install.
Alternatively, install bower globally with npm install -g bower and run bower install.