That's a great suggestion, jib71, thank you very much for it. I just hope to find something reasonable around Kansai airport, but a brief look on hotels.com earlier was not very encouraging. I thought that Osaka, being marginally better known than Kobe (in my brain anyway), was probably more deserving of a visit than Kobe. I have always associated Kobe with earthquakes and beef, quite an odd combination. Reading various threads here it seems that Osaka is not a place to get that excited about. But people say the same about Milan, and I love it there! Given the time frame, I think your suggestion represents a very intelligent use of time and less time wasted sitting in buses or trains.

Many thanks to nishimark above, too, it's very good to have that information, especially about the bus.