I take a 15 gallon (swimming pool chlorine bucket) that has a water proof screw on lid - drill two 3/4" holes in the side and install a boat style live well pump outside the bucket with a detachable cigaret lighter power cord - we can transport bait to & from the surf or boat and carry it in the suburban without worrying about spilling it
5 Gallon bucket, aerator. We try to keep the bucket in the shade and will most of the time throw a frozen 20 oz soda bottle in there at some point during the day. I will bring them inside overnight and use a cheap aquarium pump once I have electricity.
Find an old metal grocery cart w/wheels still in tact. Take it out with your other tackle in the back of your truck.
Then roll it into the surf deep enough so the water level submerges the bottom of the grating about 6 inches. Use bait large enough so they can't swim out between the holes! CF?
I fish with croaker alot in the surf. All I do is put them in one of those big 15 gallon plastic laundry baskets/storage bin deals and put an little cheap $20 aerator. If its really hot I will put some frozen water bottles in there. Have kept croaker and shrimp alive for 2 days that way.