Paul played lead guitar on Drive My Car. George played bass.
As far as I know, Paul played bass on "Drive My Car", though it's also true that Paul played the solo with a slide guitar.
I think there's an usual confusion about George playing bass on "Drive My Car", because of this George's quote from 1977:
"If Paul had written a song, he'd learn all the parts and then come in the studio and say 'Do this.' He'd never give you the opportunity to come out with something. But on 'Drive My Car' I just played the line, which is really like a lick off 'Respect,' you know, the Otis Redding version. And I played the line on the guitar and Paul laid that with me on the bass. We laid that track down like that. We played the lead part later on top of it."
I think the phrase "with me on the bass" was misunderstood. I think George meant that he played the line on the guitar, and Paul did the same with the bass, as it can be heard in the song.