At any time, you can switch to invisible mode. Going invisible hides you completely for the duration of your drive. You won't be seen on the map, you'll appear to friends as "offline," and any reports you make during your drive will be seen by others as if sent by "anonymous."
Note that in invisible mode you still get points as usual. You can go invisible by tapping the Menu, and selecting My Waze:
Then enable the Go Invisible toggle.
Please note that you'll remain invisible only for the duration of your current session. Next time you start Waze, you'll automatically return to being visible.