The van runs a continuous loop--Carnival port (if they have a ship in), Disney port, then the "store." It takes about 15-20 minutes with loading bags, etc. On really busy days, they will sometimes have 2 shuttles...they did on our day. This is on the return days. On departure days, it's the same thing only they will stop at the terminal that the passengers are going to--if everyone is Disney, you won't visit the Carnival port.
We had the smaller shuttle all to our group of 6. It would have held a couple more, but that's the way the driver set it up. My teens had the luggage loaded by the time I came out from returning the car. From there, it was 5-10 minutes till we were at the port.
SO...your longest wait till be on the return, max of about 20 minutes. We had NO waiting at the "store" at all. We had exactly the same experience at Budget too--2 shuttles, no waiting.