You can buy battery powered air pumps, as mentioned by others previously. These can sit in the car and blow bubbles into the buckets of water to help keep the oxygen levels high.
You can buy a power inverter from most auto stores. These plug into a car's cigarette lighter and convert the 12 volt power from the car, into 220-240 volt (whatever your country has) power to run a normal air pump that plugs into a power point in your house. You plug a normal air pump into the power inverter and run some airlines to the buckets of fish.
If you do get portable air pumps, you can drill a small hole in the lid to put the airline in and put a plastic multi-coloured airstone on the other end. Some of the plastic airstones have a small weight in the bottom and are great because they hold the airstone down.
If you don't have the pumps, it isn't a major issue, but fish do travel better with aeration.
Have the buckets of fish about 2/3s full of water.
Keep the buckets of fish in the shade at all times. If the weather is warm, have the car's air-conditioner on so the inside of the car doesn't heat up and cook the fish.