I believe you get rest Exp while in a Sanctuary at the same rate regardless of if you are logged in or not.
I think the max amount of rest-exp you can have is 1.5 full bars. Note that this equates to a larger amount of points at high levels than at low levels.

Rest exp does not apply to all Exp rewards. It only applies to Exp gained for monster kills, or for Exp awarded for crafting/gathering items.
So if you have many sources of Exp which do not benefit from rest-exp, then your rested Exp will be used up at a much slower rate than if all of them did benefit from rested exp.