Sue,
The mount that I linked above is the same one that I have and, yes, it does have angles and "teeth" where it would fit around the bar/mirror. Normally I guess those teeth bite into the metal to stop the mount from rotating, but I didn't want to eff my basket up so I cut out a strip of black rubber, wrapped that around the basket bar, and then clamped the mount over that. That install has been great so far with 70+ mph highway speeds and lots of bouncing around off road with no movement of the antenna....and no damage to the basket bar.
I did go with the four bolt model just to make sure that I could "custom" fit it securely where I wanted to.
Glad I could help.
"The major difference between a thing that might go wrong and a thing that cannot possibly go wrong is that when a thing that cannot possibly go wrong goes wrong, it usually turns out to be impossible to get at or repair."
-Douglas Adams, Mostly Harmless