I've never used Priceline (not yet anyway but soon) but the idea is that to get discount fares, you book late when they are trying to finish filling the ship. If they fill the ship with normal bookings, you are not going to be getting any discount over what you would get just calling the cruise line up and booking the cruise. So I guess I'm saying not to count on getting a cheap cruise and not book it normally if you have your heart set on going on the cruise. If you wait, the cruise may fill up and you won't get on. Panama cruises are popular and they fill up quick.
So you also run the risk of not getting on the cruise at all. AND April is a big cruise month (spring break) which further reduces your chances of getting a last minute booking.
They normally "close out" the cruise 30 days in advance. Meaning that they assign the "to be assigned" cabins then and create their preliminary manifests for the cruise. My guess is then they would release any open space to Priceline for sale at cheaper rates to fill the ship.
You can go ahead and try the priceline bid now and see if they take it. Go to the cruise website and price it out for what you see the cheapest cabin at and then bid lower and see if you get it. DON'T bid at the cheapest cabin price expecting a balcony....
Good luck, come back and let us know how it goes, I'm curious to see what happens.
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