Collapsing Sidebar with Bootstrap

Bootstrap 3

Yes, it’s possible. This “off-canvas” example should help to get you started.

https://codeply.com/p/esYgHWB2zJ

Basically you need to wrap the layout in an outer div, and use media queries to toggle the layout on smaller screens.

/* collapsed sidebar styles */
@media screen and (max-width: 767px) {
  .row-offcanvas {
    position: relative;
    -webkit-transition: all 0.25s ease-out;
    -moz-transition: all 0.25s ease-out;
    transition: all 0.25s ease-out;
  }
  .row-offcanvas-right
  .sidebar-offcanvas {
    right: -41.6%;
  }

  .row-offcanvas-left
  .sidebar-offcanvas {
    left: -41.6%;
  }
  .row-offcanvas-right.active {
    right: 41.6%;
  }
  .row-offcanvas-left.active {
    left: 41.6%;
  }
  .sidebar-offcanvas {
    position: absolute;
    top: 0;
    width: 41.6%;
  }
  #sidebar {
    padding-top:0;
  }
}

Also, there are several more Bootstrap sidebar examples here

Bootstrap 4

Create a responsive navbar sidebar “drawer” in Bootstrap 4?