They don't have their own shuttle service like Disney's Magical Express (which is free), but you can arrange airport shuttle service when you book through Universal for a cost. When I booked through Universal last year, they asked if I needed shuttle service and I said yes. They made all of the arrangements for me. It's also an option if you book on-line. They use Quick Transportation, which is similar to Mears.
You could easily do it yourself by googling Mears or Quick Transportation, but if it's easier to have them work it into your package, they will.