Although a fair bit slower than the train, it would perhaps be an idea if you don't want - or can't be bothered - to find your own way from the railway station in Naples to the harbour there.
No surprise perhaps that it's much as described in the first post of this thread from last year...
(Nothing as yet for the 'Train+Hydrofoil' scheme that's also mentioned there - but any such announcement may come at the same time as Trenitalia's summer schedules).
The 2011 details, but again only in Italian, are here...
Essentially though... one bus daily, from 17 June to 11 September, which leaves Rome at 09:00 - from near Termini station - to arrive at the Beverello hydrofoil quay in Naples around 11:45, where you're put onto the next crossing to your destination here on the island.
On the way back, it leaves Naples Mergellina at 17:00, does a pickup at Beverello, and then gets to Rome for 20:10-ish.
Rome – Forio or vice versa: One way, Mon/Thurs €47; One way, Fri/Sun €50; Both ways, Mon/Thurs €88 (not available Fri/Sun)
Rome – Ischia Porto or vice versa: One way, Mon/Thurs €46; One way, Fri/Sun €49; Both ways, Mon/Thurs €86 (not available Fri/Sun)