Great discussion here!
Two points:
First, Michael drove because the bodyguard needed to be able to constantly look around in all directions in case assassins were lurking or following. And he needed to have his hands free to protect Michael in case of attack. This wouldn't have been possible if the bodyguard had been driving.

Second, as Michael told Frankie, his objective was to keep Roth relaxed, confident in their deal. That's why Michael or Tom) would have let Roth know he was coming. And, in any event, Johnny Ola had met Michael and the bodyguard to guide them to Roth's place--which confirms that Roth had at least some advance notice.

FFC's fanatical attention to deal is evident all over this scene. One example is Michael driving. An average director would have the bodyguard driving, like a chauffeur, with Michael in back. But FFC wanted to emphasize the seriousness of the threat to Michael by staging this seeming anomaly. Another example is their cars. Johnny Ola's driving a '58 Chrysler New Yorker--probably Roth's car, exactly what a rich Jewish guy of that era would drive (rich Italians of that era liked Cads, rich Irish liked Lincolns ;)). Michael's car is a '58 Ford Custom 300 in original two-tone colors--exactly what Mr. Avis would have rented to him in late '58. (Others have pointed out that the Ford had a later-dated Florida inspection sticker in the windshield.)