We just drove. The bus thing was confusing to us. We left Herculaneum and followed the signs. Once on the road on Vesuvius, there are cute places to stop and eat, but we kept going. The drive was very curvy and narrow, but the view was beautiful. As beautiful as a cloudy day could be at least. I imagine on a sunny day, this would have been spectacular.
We parked at the "entrance" where you can buy souvenirs. We may have had to buy a pass, but I can't recall. despite the fact that visibility was at 10 feet, the place was hopping with people walking in to see if they could get a peek into the cone and see something exciting like lava or at least a big hole.
It was a comfortable walk along a wide road. We were very wet from walking inside of a cloud, but it was still a good temperature. We finally stopped at what might be the top - the rim of the volcano - and bought something at the one of the gift huts at the top. Postcards promised exciting views, but the reality of the day was going to be cloudy. We never saw more than a few feet into the volcano.