I am trying to do a site using twitter bootstrap. I am having relatively less menus, so it kind of fits within the 768px display also. But in bootstrap by default, the menu
You can customize Twitter Bootstrap css compiling it from sass-twitter-bootstrap scss files and setting $navbarCollapseWidth in _variables.scss to your desired value...
Edit
As @Accipheran stated in the comments, for Bootstrap 3.x the name of the variable you should set is $grid-float-breakpoint.