Bear riding ceremony?

The discussion on flagellents and the Penitentes of New Mexico reminded me of this.

In Richard Bradford’s novel “Red Sky at Morning”, set in New Mexico, he has a section involving a Christmas celebration in a remote Spanish-speaking village where the people are members of an unapproved offshoot Catholic sect. A reenactment of the nativity takes place, with an interaction between the pregnant woman playing the part of the Virgin Mary and a chained live bear:

(The woman’s dress is wet because earlier in the ceremony when she was enacting getting turned away from the inn, a bucket of water was thrown on her)

Is Bradford describing a ceremony that is actually practiced? After this point, its “normal” progress is interrupted by an action by the character in the book. I can’t find any references for it. Bradford seems to use authentic settings, but this incident wasn’t the central point of the book - he was essentially using it as a plot device in what is a “coming of age” story.