Twitter's Bootstrap is responsive by default. This include all components and the grid(s).
To find your answer, please first study http://getbootstrap.com/css/#grid
Twitter's Bootstrap defines four grids. The largest grid has a max container 
size of 1170px.
The large (col-lg-*) is bound by:
/* Large devices (large desktops, 1200px and up) */
@media (min-width: @screen-lg-min) { ... }
Your design requires a larger grid, for at least 1920px and up.
Where 1920x1080 seems to be an industrial standard: http://en.wikipedia.org/wiki/1080p
According Bootstrap's grid definitions, i expect you should extend the grids with a larger grid. See also:
See also Bootstrap 3 - 940px width grid?, 
Twitter's Bootstrap 3 grid, changing breakpoint and removing padding
To add and extra grid, download Bootstrap's LESS files from: https://github.com/twbs/bootstrap/tree/master/less, add a extra grid() and recompile your CSS.
In grid.less replace:
//or define in variables.less 
@screen-superlg: 1920px;
@screen-superlg-min: @screen-lg;
// Large screen / wide desktop
//or define in variables.less 
@container-superlarge-desktop:      ((1860px + @grid-gutter-width));
@container-superlg:                 @container-superlarge-desktop;
.container {
  .container-fixed();
  @media (min-width: @screen-sm) {
    width: @container-sm;
  }
  @media (min-width: @screen-md) {
    width: @container-md;
  }
  @media (min-width: @screen-lg-min) {
    width: @container-lg;
  }
  /* Larger devices (HD TV, 1920px and up) */
  @media (min-width: @screen-superlg-min) {
    width: @container-superlg;
  }
}
and add:
//  Super Large grid
//
// Columns, offsets, pushes, and pulls for the hd tv device range.
@screen-lg-max:              (@screen-superlg-min - 1); // define in variables.less
@media (min-width: @screen-superlg-min) {
  .make-grid-columns-float(superlg);
  .make-grid(@grid-columns, superlg, width);
  .make-grid(@grid-columns, superlg, pull);
  .make-grid(@grid-columns, superlg, push);
  .make-grid(@grid-columns, superlg, offset);
}
After doing this you can use the new Super Large grid by using col-superlg-* grid column classes.
After this you should also have te extend the Responsive utilities (http://getbootstrap.com/css/#responsive-utilities) defined in less/responsive-utilities.less.