Built in Slide Cart support
We are actually the developers behind the #1 cart drawer app on Shopify Slide Cart. Slide Cart works with Super Bar out of the box, and I'd highly recommend checking it out.
Using another app or a theme's cart drawer
Using a third party cart drawer will be a little more difficult. If you're not familiar with your cart drawers workings you'll have to contact its developers, but the basic steps go like this...
Change the add behavior
Start by changing your add to cart behavior to nothing. This will stop any cart/checkout redirects that may be happening from Super Bar.