How is bootstrap holding back when it comes to PHP an MySQL? JS, sure, I can understand, since most of it is just using their API, but how is it holding me back when it comes to PHP and MySQL?

Because it is not necessary to learn PHP/MySQL. And if you add JS, even worst, don't use bootstrap at all. Don't use any PHP framework too at this stage.

It's a framework that makes things look decent enough by default though.

If your goal is to learn something other than web design (eg. PHP / MySQL), then surely you want something that can do things well in that department by default so you don't have to mess around with it too much?

That was my intention: Learning the practical side of PHP and MySQL, without having to deal with too much design and markup. At the same time I didn't want my project to like a POS, which is the main reason I used Bootstrap.