This morning he/she was back again.
Since I don't know whether it's a male or a female, I'm going to refer to it from now on as "it".
It was enjoying the cold water, splashing and ducking it's head.
And then, suddenly, a SECOND Towhee arrived.
The first one checked out the second one but it soon became clear they were acquainted and it went back to its bathing.
The late arrival seemed content to just sit in the cold bath water but the constant splashing of the other one showering water on it finally caused it to depart.
The first bird continued violently splashing and throwing water over itself for some time.
Finally it was apparently satisfied and departed as well.
And so, once again, the bath is quiet.
I can only wonder what will come next.