Change bootstrap navbar collapse breakpoint without using LESS

You have to write a specific media query for this, from your question, below 768px, the navbar will collapse, so apply it above 768px and below 1000px, just like that:

@media (min-width: 768px) and (max-width: 1000px) {
   .collapse {
       display: none !important;
   }
}

This will hide the navbar collapse until the default occurrence of the bootstrap unit. As the collapse class flips the inner assets inside navbar collapse will be automatically hidden, like wise you have to set your css as you desired design.

2018 UPDATE

Bootstrap 4

Changing the navbar breakpoint is easier in Bootstrap 4 using the navbar-expand-* classes:

<nav class="navbar fixed-top navbar-expand-sm">..</nav>

• navbar-expand-sm = mobile menu on xs screens <576px
• navbar-expand-md = mobile menu on sm screens <768px
• navbar-expand-lg = mobile menu on md screens <992px
• navbar-expand-xl = mobile menu on lg screens <1200px
• navbar-expand = never use mobile menu
• (no expand class) = always use mobile menu

If you exclude navbar-expand-* the mobile menu will be used at all widths. Here's a demo of all 6 navbar states: Bootstrap 4 Navbar Example

You can also use a custom breakpoint (???px) by adding a little CSS. For example, here's 1300px..

@media (min-width: 1300px){
    .navbar-expand-custom {
        flex-direction: row;
        flex-wrap: nowrap;
        justify-content: flex-start;
    }
    .navbar-expand-custom .navbar-nav {
        flex-direction: row;
    }
    .navbar-expand-custom .dropdown-menu {
        position: absolute;
    }
    .navbar-expand-custom .nav-link {
        padding-right: .5rem;
        padding-left: .5rem;
    }
    .navbar-expand-custom > .container {
        flex-wrap: nowrap;
    }
    .navbar-expand-custom .navbar-collapse {
        display: flex!important;
        flex-basis: auto;
    }
    .navbar-expand-custom .navbar-toggler {
        display: none;
    }
}

Bootstrap 4 Custom Navbar Breakpoint
Bootstrap 4 Navbar Breakpoint Examples

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**Bootstrap 3**

For Bootstrap 3.3.x, here is the working CSS to override the navbar breakpoint. Change 991px to the pixel dimension of the point at which you want the navbar to collapse...

@media (max-width: 991px) {
  .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;
  }
}

Working example for 991px: http://www.bootply.com/j7XJuaE5v6
Working example for 1200px: https://www.codeply.com/go/VsYaOLzfb4 (with search form)

Note: The above works for anything over 768px. If you need to change it to less than 768px the example of less than 768px is here.

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in bootstrap3, change this variable @grid-float-breakpoint to the one you need. The default value is 768px