If you have JR Rail Pass you can ride from and to Izumo and Hiroshima.
There are few buses between Izumo and Hiroshima. Valid only for JR operated Bus. It's only less than 3 hours ride.
There is sleeper train sunrise Izumo! It has shower, cafe seats, private rooms etc. You can reserve seat a month in advance.
For both train and bus schedule check this site. http://www.hyperdia.com/en/