The JR West Kansai four-day Pass would fit he bill.
http://www.westjr.co.jp/english/travel/jrp/index.htmlThis pass allows you to use the Shinkansen Nozomi train between Shin-Osaka and Hiroshima, unlike the Japan Railpass. It expires on the day you head back to Osaka.
When you get around Osaka, I'd suggest you to obtain the Icoca, a prepaid IC pass.
http://en.wikipedia.org/wiki/ICOCA
Even though there is no discount on it, the fares are automatically deducted when you clear the exit turnstile by holdinging it over the sensor.
In order to get back to KIX from Osaka City, you might take the limousine bus from Umeda, or the Nankai Line train from Namba. The prices are very reasonable.
http://gutereise09.blogspot.com/2008/09/limousine-bus-f...
http://gutereise09.blogspot.com/2008/09/info-on-nankai-...