Depending on the number in your group, there are 5 choices.
Mears Transportation $16 PP, reserve the night before, shared service, scheduled service. You can scehdule your ride back to your Disney resort by phone two hours before you wish to depart.
Taxi - There are always taxis quickly available near your resort Bell Services stand, and there is a taxi stand at Universal. Unknown on cost. Most taxis take 4 - 7 passengers for the same cost.
Towncar/Towncar Van - Reserve in advance, approximately $70 - $85 RT for 4 - 10 passengers. Advanced scheduling of times and service, so if your plans change dramatically and you have to leave early, the driver might be engaged elswhere.
Lynx bus system. Very cheap, less than $5 per person, but takes approximately 3 hours each way with a bus transfer downtown.
One day rental car from an agency on or near Disney property.
Alamo/National has offices at the Dolphin and the Car Care Center, there is an agency at one of the hotels on Hotel Plaza Boulevard within walking distance of DTD. Can be as little as $25 for 24 hours plus gas/plus $11 parking fee at Universal.