I have a party of 5 for a Cozimel cruise on March 20,2007. Transfers will be $200 from the airport and back.
First of all, you are doing the right thing by flying in the day before the cruise. Where are you coming from? The Port Of Mobile is a great facility, and is near the downtown Mobile area.
The Renaissance Riverview Plaza Hotel
is just a stone's throw from the pier, and they mention a free shuttle for their "park and cruise" package. I doubt they'll want proof you are parked at their hotel, and you can use their shuttle bus. A cab from the hotel to MOB is around $26 one-way. You'd need two cabs with 5 people, but that looks to be around $100 total for getting to the hotel, and then back to the airport on debarkation day.
I'd call the hotel and ask about the shuttle. The rooms aren't especially cheap, but it is a nice hotel.
Whatever you do, please avoid the Best Western Battleship Inn. We stayed there a couple years ago and it is a dump. Our room had bedbugs and we all got bitten.