There are lots of gospel images associated with the River Jordan in Israel. I think the biggest association is from the Christian religion - with John the Bapist, baptizing all who came to the river and repented for their sins.
While I am sure the River Jordan is still an huge religious attraction for Christians visiting the Holy Land, it has become a different kind of attraction for modern Israelis. Rafting on the Jordan has become a popular activity.
Unlike rafting on the Colorado River in the United States, rafting on the Jordan is a much gentler experience. It is more of a relaxed float, where river runners sit back and enjoy the ride. I believe the starting point for most "rafters" is where the Sea of Galilee feeds into the Jordan. They say it takes from 1-2 hours to go down the river. Maybe a little longer if you stop for a picnic lunch.
There are several companies that provide all the gear you need for your River Jordan experience - ranging from tubes to kayaks. I believe that part of the service usually includes a return trip by bus to where you parked your car.
Floating down the River Jordan sounds like a nice way to spend an afternoon. However, I don't know if it would be an ideal activity for a lone traveler? For some reason, it seems better suited for families or groups of friends. But, then again, if I am in that area, I might still check it out. However, this might be one of those activities best done in the summer. Winter might be a tad chilly to run the river.