re: Live well - Keeping bait alive

I typically use cut bait with heavy spinning setups and cast out from a Galveston jetty targeting redfish and blacktips. This time I'll be bringing a lighter setup too to go for trout and I had the same question as the OP.

We go to a bait shop on Galveston island and have gotten live bait in a bucket with an oxygen tablet but the fish/shrimp always die too quickly. Is there anything we can do to make them last longer or is a bucket without a pump always doomed to fail?

And how effective can a dead shrimp or fish be for trout? I'm just trying to figure out fishing with under a popping cork. Is that possible with dead bait?