Currently there is a promotion through the Walt Disney Travel Company where guests can get tickets to Universal Studios with complimentary shuttle. Other than that, there is no set transportation between Anaheim and Universal Studios.
If you want to get to City Walk at Universal Studios, your best bet is to rent a car. You could also take a more roundabout method, and that would be to take the bus on Harbor Blvd to the Fullerton Train Station, take a bus or train to the Union Station in Downtown Los Angeles, and then take the metro from there to Universal Studios. I don't know the timing, but it could be done.
If like TribeFan said, you really mean Downtown Disney, then it ends (or begins) at the Disneyland Hotel.