The ferry is far and away the best way to get from Matsuyama to Hiroshima. There's 2 kinds, fast and slow. Slow takes 2 hours 40 minutes and is about 2700 yen, fast is about an hour and is 5900 yen. There's a bus that goes out to the port from town, leaves from the city station.
Website for the ferry fwiw, sorry all Japanese
http://www.ishizakikisen.co.jp/