My bots with zero plus exp boosts other than nephalem stacks and full looting on, get around 10-15mil exp/hour.
According to the internet, you need 10,454,400,000 exp to get from 1-100
That means you will need about 700-1000 hours of botting, or a bit more than a month of straight 24/7 leveling.
I'd say if you're botting cautiously and only running around ~12 hours per day, it would take 3 months with full looting. You could probably drop the time down to one month if you turn off most loots or you invest in some +exp gear. If you really go hardcore and go 24/7 with exp gear and no looting you could probably do it in 2 weeks.