I have flown into AUH and driven to DXB many times, but always by taxi.
There is a limousine service from AUH that is pretty good. The cars are silver Mercedes, leather seats, air con, English speaking drivers etc.
It costs about 240AED and takes about 90 minutes.

The limousine company is www.fastuae.com

They also have a branch in Dubai so you can order a return car too.