From my experience, many Bassets are poor car-travellers. We have had those who don't mind (our second hound, when we didn't have a proper dog-car!) would lie across the back seat on his back, just like he'd do on the sofa!! Chilled or what. On the other hand we've had those who'd upchuck the moment we put them into the car. One particularly bad one was cured after he ingested a grass seed which took forever before it pointed and could be lanced and removed. Involving a load of vet trips. By the time that was resolved, his car travel problems were too.
Once I realised what it was with Bassets and cars, I'd start from a very early age getting them used to the concept of being in the car, and then with it moving. I'd try everything from feeding, to not feeding (I tended to prefer giving them a bit to eat as what came back wasn't just 'water'!!), from travel pills (which would come back) to no travel pills.
Over all the years, with sick Bassets in cars, it's a wonder I'm not the same. We always travel with what we call a 'sick kit' - loads of paper towels and change of bedding.
I recommend you do NOT let him get anywhere near windows (conjunctivitis is a real risk) even if you have to crank them down - no more than an inch. And you will need to get appropriate car transport (we had to sell our MG(S) once we were with Basset) - an 'estate' (UK) or 'wagon' and use a crate, covered. Mine who suffered were better travelling at night so covering a crate in daytime would make it dark(er). But do keep at it. Hopefully on good surface roads at first and preferably motorways/freeways so the engine note was more constant and no corners.