Welcome to the forum. I was from the Phoenix area, but my company transferred me to Texas.
There is a monthly motorbike ride in Tucson, beginning at the big park east of downtown on Broadway.
Spooky Tooth hosts motorized bicycle races at the local go kart track (near the fairgrounds) a few times a year.
Local group rides are held every spring and fall after the bicycle swap meet on 6th Ave(?) (El Swap de Tucson, etc)
Sorry I don't have the details.
You're living in a great place to enjoy a motorized bike.