How many in your group?? If there are 4 or 5 in your party, renting a small car for the day might be your most economical solution. Try
Alamo/National at the Car Care Center or the Dolphin.
If there are only 2 or 3 then Mears is the most economical solution at $16 PP RT.
The day before you wish to go to Universal, dial "0" from your Disney resort room phone or any house phone.
When the Disney Operator picks up, ask to be transferred to Mears.
When the Mears Operator picks up, tell them you wish to go to Universal the next day, how many in your party, what resort you are staying at, and approximately what time you wish to leave.
They will give you a pickup time and location.
Arrive at the pickup location the next morning about 10 minutes before the stated time.
When the Mears Van/Bus arrives, you will pay the driver $16 PP CASH and will be transported to Universal. (This is a shared ride, so there may be other stops.)
When you arrive at Universal, the driver will give you a voucher for your return trip. You can schedule your pickup time then, or call the number on your voucher 2 hours before you wish to leave Universal.
At the appointed pickup time be at the same location you were dropped off and you will be returned to your resort. (This is a shared ride, so there may be other stops.)
If you decide you want to use the Mears service and want to use a credit card for the transportation, stop at the Mears desk at the airport BEFORE going to the Magical Express desk/rental car/towncar/taxi, etc. and purchase RT Universal transfers in advance for your party.
You still have to call the day before to make the actual transportation arrangements.