You mean without linking it to Codecademy's 'bubbles.js' script? Sure, it's certainly possible. But I wouldn't recommend it because it requires a lot of code. If you want to see the JS code that Codecademy made for you, just copy the URL into the address bar at the top of your browser and hit enter - It will come up with some text which will be the code... there's a lot.
Also, jQuery is used, so if you wanted to do this without it, it would require much more code, so overall I don't recommend doing it the long way, just keep to what you have and brag about your supreme coding skills