How long really depends on how the mange progresses. It is likely to look worse before it looks better. That's quite logical if you think about it: hair loss occurs long after the follicules are irreversibly damaged. Damage that happened to hair follicules last week (for example) won't show as actual hair loss for a month or two. So what happens over the next month is going to be predominantly the result of what damage (or lack of damage!) happened last month. Does that make sense to you?
Put another way, if it starts looking better straight away, then it's because her immune system has already started recovery.
Thus, you need to monitor her condition. If it starts to look a little worse, don't panic - that's to be expected, and is the result of damage incurred before this point. If it starts to look dramatically worse though, then you should consult with your vet and consider treating it. And, of course, if there is no sign of any improvement at all in 3-4 months time, then that could be another reason for considering treatment.
Put another way, if it starts looking better straight away, then it's because her immune system has already started recovery.
Thus, you need to monitor her condition. If it starts to look a little worse, don't panic - that's to be expected, and is the result of damage incurred before this point. If it starts to look dramatically worse though, then you should consult with your vet and consider treating it. And, of course, if there is no sign of any improvement at all in 3-4 months time, then that could be another reason for considering treatment.