Scott Bradley at MGM studios in Hollywood was the musical director for those cartoons, so it would have been a West Coast studio band. The vocals sound quite a bit like Slim Gaillard, so maybe it was him or Slam Stewart? More likely the vocals were by the actor who voiced "Droopy" (made by the same folks) and a studio player whose name is lost to us played that bass. He is however, in that clip, squarely in Slam-land as far as rhythmic drive and tone. Haven't heard this in at least twenty-five years. This may very well have been one of the first things that made me want to pick up a bass. Thanks for sharing!
So... the upshot is that if you want to hear more playing like this, pick up some Slam Stewart. There are a few retrospectives of the Slim and Slam sides on CD. If you can find a copy of the 1945 town hall concert, reissued on Commodore, where he does a set as a duo with Don Byas, I highly recommend it. Checking out Milt Hinton's recordings with Cab Calloway in the 30's or Pops Foster with Louis Armstrong from about the same era will fill that jones, too.