This is a nice one.
Bootstrap is a nice framework, the great advantage of using it is that it saves you a lot of time while building a responsive web site (the same can be said of other css frameworks out there).
The drawback is that the web sites coming out in the last years very often looks the same, all of them have the same navbar and the same menu behavior which collapses for extra-small devices, showing a menu button which reveals the content when pressed.
A good way to differentiate your web site from the others could be a change in the menu collapsing behavior.
Datmenu is a nice responsive menu plugin for Wordpress, so the idea is ...