I'd been the most paranoid person about leaving the garmin on the bike but that day was insane riding the tandem in pouring rain, solo, trying to make a ferry ... Anyway, that was yet another problem - I'd stick the thing in my jersey pocket, pull it out and all the fields were changed due to touch screen.
There's a screen lock on the 800 for that, which they eliminated in the 810.
If I turned it off I'd forget to hit "start" and there's no reminder when you're mid ride - at least I never got one. My preference would be to have a device that is on if I'm moving.
You're better off just leaving it running. Software will figure out average moving speed, etc. if you're interested.