There is a (Mears run) Universal shuttle from the airport to the resorts. No, it's not free, but it was pretty efficient. It may have cost a bit more than a rideshare/taxi but definitely had more luggage space and less unpredictability. I'm on vacation, if I can handle logistics in advance, why wouldn't I? Yes, you may have to make a couple of stops, but so what? We saw it as an opportunity to check out hotels we weren't staying at (and really, 2 extra stops only added a few minutes to the trip).
You check-in near the rental car counters. They will even give you your park tickets there instead of having to pick them up at the desk at your hotel. Then you wait at the bus loading area. They'll direct you to which bus is going to what hotel(s) and away you go.
The return from the resort to the airport was just as efficient. They give you a time for pick up (usually 2-3 hours before your flight). It was very stress-free - no wondering if the Uber is going to cancel or if I'm going to have to hold my suitcase in my lap.