(never have stayed there) from the airport but I did take Transtar to the general vicinity of this hotel last year.
Last year, we boarded a Transtar shuttle which dropped off a first set of passengers straight from the Orlando airport to a hotel that was very near the HRH/within the same Universal Studios area; it took us around '20-25 min. approximately' to get there.
Also, since you are riding with others, it is my guess that when traveling, the driver is first likely to drop off the passengers whose hotel happens to be the first one he/she reaches initially enroute (so as not to unnecessarily backtrack).
There were two other sets of passengers on our van besides us (making it three in all) so in total we made three different hotels stops because none of the parties happened to be staying at the same hotel(s).
So, I would think that the direct number of stops that will be made before you actually reach the HRH is going to be highly dependent upon how many other parties you're riding along with, whether or not some are staying at the same exact hotel, along with the particular hotel the driver strategically arrives at first when traveling.
Hope these helps.