If you really understanding every aspect of bootstrap, you can use any CMS. It does not matter if a theme support bootstrap or not, however it would be a lot easier. Look for a theme that closely resemble your design. Draw out the structure of that theme..
For example
Code:
<body>
<div class=topmenu>
<div class=subtop></div>
</div>
<div class=body>
<div class=subbody></div>
</div>
<div class=footer>
<div class=subfooter></div>
</div>
</body>
In my schematic it would look like something like this.
-->div topmenu (css property)
---->div subtop (css property)
-->div body (css property)
---->div subbody (css property)
-->div footer (css property)
---->div subfooter (css property)
After having the schematic drawing of the theme I can remove their css class and use the correct class from bootstap. I can convert their class name into ID for structure data. Therefore I can have ID to identify my tags. This I can structure my tags while using bootstrap class as my rendering property.
You can built your CMS but a good CMS does not take one month to build. It is quite a bit longer. However if you can make one, there is a lot of thing you can do with it. Nevertheless take into consideration that it may have bugs. It may have security vulnerability.