How far is it from Pompeii to Amalfi Coast? And are there any busses or trains between the two?

Pompeii is situated on one side of the Salerno peninsula, and the Amalfi coast is on the other. There are a variety of ways to go from the Pompeii to the Amalfi coast. Taking the coast road from Pompeii to Sorrento allows you to take the Amalfi coastal road from above Sorrento. From nearby Castellamare, a different road, climbs up over the top of the peninsula bringing you down to the Coast near to Amalfi. A third option exists by heading south to Salerno and picking up the Amalfi coastal road there.

You are pretty much limited to ground transport using your own private vehicle or buses from Sorrento (the latter not for the faint hearted!) Theoretically you could go by train to Salerno and then catch a boat around to Amalfi or Positano. An additional option exists if you go in the opposite direction to the port of Naples. From Naples, you could catch a boat to most points in the Bay of Naples.

On additional thought: If you are planning a tour in the Bay of Naples, one of the best selling tours on board cruise ships is the Pompeii, Capri Amalfi Coast tour. Whilst this is a very full overview of the area, you should know that this is really a lot to see in one day. At a pinch, with the right organisation, you are comfortably able to see Pompeii and the Amalfi coast OR Capri in a day. If you are arriving by cruise ship, then it is possible to organize this in advance with a local agent.