Day tours to Kumamoto from Fukuoka via Bus

I am purchasing a 7 day Japan Railpass but plan to use it after a three night stay in Fukuoka. Are there bus tours to Kumamoto from Fukuoka?
I am also interested in stopping to experience the roadside stalls where flowers, fruit, bentos and other omiyage can be purchased.

To see what? The castle? Aso? Some Japanese tour agencies based in Fukuoka might offer such tours for a Japanese clientele.

But I recommend to travel there yourself. It is easy. With the shinkansen it takes just half an hour from Fukuoka's Hakata Station to Kumamoto Station. By bus it would take close to two hours. A shinkansen round trip with a 2-mai kippu costs 7000 yen.

Since I had two days in Fukuoka I wanted to sightsee beyond Hakata area. I plan to start using the railpass from Day 4 of the trip extending to the end on Day 11 when I will be back in Fukuoka. Will travel from Hakata Station to Osaka on to Tokyo, back down through Hiroshima and spend night and 1-1/2 days in Hakata before flying out from Fukuoka. I am hoping the hotel will have brochures advertising day tours around the city and beyond. Appreciate your input.

From Hakata, if you only had 2 days, use one day for Hakata and another day for Dazaifu shrine and/or Yanagawa by Nishitetsu rail. Yanagawa is great for hiking around the small town, delicious grilled eel meal at a beautiful garden property "Ohana" (http://www.ohana.co.jp/e/index.html), Donko canal boat ride, etc.
If you want to go farther to onsen(best to experience while in Kyushu), castle, garden, etc. like Yufuin, Beppu, Kurokawa, Nagasaki, Kumamoto, etc.
Use SunQ Bus Pass.
http://www.sunqpass.jp/english/route/index.html
Or JR Kyushu Pass: You can buy one in Japan.
http://www.japan-guide.com/e/e2361_05.html

Very helpful response! Thank you for the links, I checked them out and will look into the unlimited bus pass which looks like I can purchase at Hakata station. My hotel is across the street from the station.

I would also look into getting a Kyushu Rail Pass. There is a 3 day as well as a 5 day version for northern Kyushu in addition to all of Kyushu. You can get it before arriving in Japan, or you can pick it up at Kokura or Hakata Station. See
http://www.jrkyushu.co.jp/english/railpass.html
To be honest, it would be a waste if you spent a whole day on Dazaifu and/or Yanagawa. The Tenmangu shrine is the only interesting thing in Dazaifu, and you will be through it in about 20-30 minutes tops. The canal boats in Yanagawa are nice too, but don't take that long either. You could spend 1-2 days seeing Fukuoka City, but if you want to know what to do with a day, I'd say use the rail pass and go see Nagasaki or Beppu for a day. They are far more interesting. You can see a good guide to Fukuoka at
http://www.tinyurl.com/see-fukuoka
and for Kumamoto see
http://www.japan-guide.com/e/e4500.html
http://wikitravel.org/en/Kumamoto
Suizenji Garden should not be missed.
Or if you want to go the whole way, see Sakurajima in Kagoshima. It's very impressive
to be at the base of a live volcano. If the weather is nice, you will see a picturesque view you will never forget.
http://www.japan-guide.com/e/e4600.html

Thank you for your recommendations. This is all very helpful. I have two days before I start to use 7 day railpass, which I have accounted for as I travel to Osaka, Tokyo back down to Hiroshima and spend last night and the next day in Fukuoka. I prefer not purchasing a 3 day rail pass so may end up spending the first two days in Hakata. I just thought if there were day tours to nearby cities, I would be prepared to look into that. BTW I am travelling with my mother and my husband and meeting up with our children in Osaka (both in mid 20s).They will be going to Summer Sonic concert in Maishima before we all head to Tokyo.