There is an interesting way of traveling between Kobe and Kansai Airports - by ferry, called the Kobe-Kansai Bay Shuttle.  English information, schedule, costs, etc., is available at  From Sannomiya (central Kobe), take the PortLiner train to Kobe Airport.  This trip takes 18 minutes.  From the airport terminal building, follow "Bay Shuttle" signs to the shuttle bus stop outside for the short trip to the ferry terminal, or walk across the parking lot to the ferry terminal.  The ferry departs every hour and only takes 30 minutes to get to Kansai Airport.  Staff members help with luggage, making this an easy-to-use service.  Upon arrival at Kansai Airport another bus shuttles passengers to the main terminal departure level.  

In the other direction, there is a ticket booth in the arrivals hall at Kansai Airport and right outside the shuttle bus picks up at Bus Stop #12 for the trip to the ferry dock.  

On board, the ferry plays videos, cycling between Japanese and English, introducing pasengers to things to see and do in Kobe.