Upvote:2
I haven't been to Agrigento in 25+ years but back then there were buses to quite a few places from Agrigento. Although we took the train from Palermo to Agrigento, we ended up going back by bus, more convenient and more choices.
Upvote:2
Rome2Rio suggests a 4h50m bus journey from Agrigento to Siracusa via Catania as your cheapest and fastest option:
Buses run several times a day and are operated by SAIS Trasporti, whose website details the itineraries and costs of all the tickets.
Alternatively, you can choose a 5h regional train journey via Caltanissetta. This itinerary is available once per day. See the Trenitalia website for options and bookings.
Finally Blablacar is a very popular car-sharing service, that works fine in Italy.