How long for a reboot of a living persona?

The same as it is for a device: the process finishes at the end of the combat turn after the process starts. So if, like most technomancers you "reboot" while you sleep (keeping your persona online while you're unconscious strikes me as a singularly bad idea) you'll be back online at the end of the combat turn after the delay you set ends.

Naturally, as you control the "power button" of your own LP you can always end the boot delay prematurely.