A webhook would be a URL you can tell bitbucket to hit when you push changes to it. That would only be useful if you set up a web app at the other end that listened to it and did something about it, which would involve a fair bit of coding.
It sounds to me like you want to be able to do "git push" for your deployments, but you don't want to lose the ability to push to github as well as pythonanywhere. Did you know you can set multiple remotes for a repository? You just name them whatever you like (the default, "origin", is just a default).
So you could set it up where
git push origin
sends your code to bitbucket, and
sends your code up to PA, and the does all the live deployment stuff as per the blog post.