You can buy a battery operated aerator for less than 10 bucks. Buy a cheap cooler or use an old one and drill a hole in the top and drop the tube with the stone on it down the hole. Just fill with your water and bait and you should be good to go. If you dont want to buy a cooler and dont have an old one you can always pick on up at yard sales for a buck or so.
Thats basically what I've done for 2 years. IN my old house I used a cooler, a reg air pump for a 40 gallon tank & bango, it worked well for goldfish & bluegills. Now that I've moved, I;ve found out the hard way that the same set up doesnt work too well in a metal shed. It gets way tooooo hot!
if you wanna make it a little fancier.. then use a good insulated cooler and a bilge or small pump. and run hose to the top and cut some slices or drill some holes into. Its a little more complicated but still pretty cheap and very effective.
I made one with a cooler, some PVC water line, and a bilge pump. It kept the bait alive for days. Next time around I will be going with a through the hull type pump though. As for filters, I have so many aquariums around that I usually have a spare sponge filter to use for it. The downside to using a cooler is that fish like shad will constantly smash into the sides and die an early death. ANyway, here are some pics of my cooler
I used to use an old igloo cooler that had the drain spout. I ran the tube through the drain spout and siliconed the crap out of it. Ran a bubble pump from Wally world on D batteries and it would keep bait til the batteries died, usually 2-3 days with good batteries, always two day trips or more.