Bootstrap CSS Breaks In SharePoint 2013

I'm developing a web app for my employer and they want it to live on SharePoint (i.e. There's no other way around this. It's set in stone).

I began developing locally, using Bootstrap, until they found a place for the app to live.

After the powers that be chose SharePoint, I moved the files over, visited the URL, and the design is broken.

Some elements are not in place and can be way off.

But locally, the app looks as it should.

Any idea as to what could be breaking the CSS?

I've already asked if we can install Bootstrap 3 for SP 2013 and was denied.