Snippet to change breakpoint of hamburger menu without needing to recompile SASS. Tested in bootstrap 3.

bootstrap-custom-menu-breakpoint.css

@media (max-width: !!!YOUR BREAKPOINT!!!) {
    .navbar-header {
        float: none;
    }
    .navbar-left,.navbar-right {
        float: none !important;
    }
    .navbar-toggle {
        display: block;
    }
    .navbar-collapse {
        border-top: 1px solid transparent;
        box-shadow: inset 0 1px 0 rgba(255,255,255,0.1);
    }
    .navbar-fixed-top {
		top: 0;
		border-width: 0 0 1px;
	}
    .navbar-collapse.collapse {
        display: none!important;
    }
    .navbar-nav {
        float: none!important;
		margin-top: 7.5px;
	}
	.navbar-nav>li {
        float: none;
    }
    .navbar-nav>li>a {
        padding-top: 10px;
        padding-bottom: 10px;
    }
    .collapse.in{
  		display:block !important;
	}
}