Bus from Hiroshima to Fukuoka or Shimonoseki

Hi guys,

I'll be in Japan in April 2016 and am looking at catching the ferry to Busan from either Shimonoseki or Fukuoka, depending on how much it costs to get to either place.

I will be in Hiroshima before catching the ferry and am looking to take a bus to keep travel costs down.

Is there a bus that runs from Hiroshima to Fukuoka or Shimonoseki?

At the moment I have only found trains and am looking at finding a cheaper mode of transport.

I've seen some posts that there is a bus to Fukuoka for 4000 yen but I can't find any sites to back this up or see times and ticket costs etc.

One old post from 2011 linked this site hiroko-group.co.jp/kanko/fukuoka/index.htm but I can't find an English translation.

Has anyone traveled from Hiroshima to either Shimonoseki or Fukuoka recently via bus?

Any info would be great thanks!