Refactor components to be more mixin-friendly.
Honestly, Bootstrap will really benefit from being easier to fit into your own markup, rather than forcing your markup to fit Bootstrap. I mean: that's what CSS is kinda all about.
Bootstrap was so painful the moment you deviate from their styles. Similar to Rails when deviating from the "rails way".
If you have been developing your site with Bootstrap to-date, then you've very likely been using their style classes throughout. For example, if you setup a grid on a page, perhaps you did something like this:
<div id="home" class="row">
<div id="content" class="span10"> </div>
<div id="sidebar" class="span2"> </div>
</div>
Upgrading is just one example, another example is attempting to use Bootstrap to style an existing application where you do not have the ability (or only a limited ability) to change the HTML, but only the ability to inject a CSS "theme".