One of the sites that I had not personally visited before was Bethany beyond Jordan, which of all the claimed locations of Jesus’ baptism by John, this one has the best claim of all. It’s become a beautiful site with various Orthodox and Catholic churches, and I actually got down in the Jordan and performed a ceremony of baptismal remembrance for various folks….
The river has various tributaries here, and they are not terribly deep in May. I sank up to my knees in mud whilst in the river……and the water was indeed cold ‘the Jordan is muddy and the Jordan is cold, chills your body by not your soul’. There were several large Oriental groups getting baptized here while we were there. I recommend a visit to this site….. What it suggests is that John the Baptizer operated on both sides of the river, and perhaps on the far side of the river mostly to stay away from Jewish authorities and the Romans….
Here are the ruins of a very ancient church, perhaps going back to the 4th century, 
What you are looking at is the walkway that led down to where persons were baptized at the Jordan, or a tributary thereof. Here’s a drawing of what the complex would have looked like originally. 
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