You'd probably have to serve two different versions of Bootstrap, one default and one with a modified variables.less
Have a look at this part of the file:
// Point at which the navbar becomes uncollapsed
@grid-float-breakpoint: @screen-sm-min;
// Point at which the navbar begins collapsing
@grid-float-breakpoint-max: (@grid-float-breakpoint - 1);
You could change it to something like this to never show the mobile menu
// Point at which the navbar becomes uncollapsed
@grid-float-breakpoint: 0%;
// Point at which the navbar begins collapsing
@grid-float-breakpoint-max: 0%;
Call the compiled CSS file maybe bootstrap-desktop.css
and then serve this CSS file instead of default if the user visits the desktop site