There are small single room sized swamp coolers you might take a look at for ideas. They tend to be about the size of a kitchen trash can. Some can connect to a water source and some need to be refilled as needed.
Under the bus presents several challenges, like how to get the water supplied/resupplied, and having the water tank and soak pads in available space and still be effective, while one big advantage is eventual water leaks are less of an issue than a roof mounted cooler.
There are 2 electrical needs, fan and water pump. The most power consumed by a swamp cooler is the fan and getting it to work is absolutely essential to keeping your cool. For a 12 volt electrical system on a vehicle an electric radiator fan can really pull the air like a tornado with multiple speeds possible. Bonus, on warn but not-so-hot days you can run just the fan for ventilation without soaking the pads.
The only other electrical power needed is for the water pump motor to soak the pads and for a vehicle that can be something like a 12 volt fuel pump or something that can handle pumping water.
One other point, coolers need to have Air In/Air Out, so letting the air out is just as important as getting the air in.