Dave is correct. I saw Budget vans last June, so I know they have them. If you want to confirm, call budget and ask (you can probably direct dial the Budget office in Port Canaveral.
The vans drop you off at teh ship and will show you where to wait on the return. You probably won't have to wait for more than 30 minutes to get a shuttle.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013