Not an official site: http://www.positano.com/en/amalfi-coast-events.
Never been there, but I assume fireworks will be performed around midnight, as normally happens in the area.
If you plan to reach Amalfi on late afternoon, have the time to see everything and be at the center of the action.
From Sorrento the only option is the driver, given that no SITA buses run after 10 PM.
No idea about the cost, I would simply negotiate the rate once in Sorrento, asking at different TA or hotel desk.