When I gazed at 渡, I spotted the “water” radical and 度, which can mean “time,” as in もう一度 (mō ichi do: one more time, again). I thought it was perfect that “time” was inside a kanji related to transience. And as 渡 has to do with ferries, my mind drifted back to Greek myths and the ferryman Charon, who rowed the souls of the newly dead across rivers to the underworld. Death and time are intimately related, so I really thought I was onto something! (Sure, ancient Greece and China aren’t intimately related, but we’ve seen cultural borrowings before. Ideas have a way of migrating (渡) around the world.)
Enough of what isn’t quite true! Henshall says that in 渡, the “water” radical represents “river.” Meanwhile, 度 here means “degree” but acts phonetically to express “span.” So we have “spanning a river,” which later came to mean “to cross over” more generally.