Materialize is not based on Bootstrap nor just a "visual layer", using both frameworks may lead to a lots of incompatibilities or at least overlap a lot as most of their functionalities are redundant (grids, menus, icons, etc).
I personally use this project Bootstrap material design which is a theme for Bootstrap and works very well.
If you don't need/want Bootstrap you can also use Material Design Lite that has been recently released by Google. It is a light CSS framework based on Material Design guidelines. Light in comparison to Angular Material or Polymer also using Material Design guidelines but part of or requiring other javascript frameworks (i.e. Angular).
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