Hi to all,
Somebody knows if there is a regular bus service between the two towns?

In May, I had to route back to Amman from Madaba, to get to Karak. When you arrive at Karak, get off at the stop before the Bus Station, It's an easy hitch-hike up to the castle.
No there isn't. It is possible to get a bus from Madaba to Dhiban, arrange a lift across Wadi Mujib and another bus from Ariha to Kerak, but these are local buses with rather vague timetables (which I do not know)
It is surely quicker to go through Amman.

Quickest way is to get a bus from Madaba to the Wihdat bus station (Mujemma al-Janoob) in Amman. Buses go from there direct to Karak. Make sure you start the trip early in the morning - 7am.
Don't get a bus from Madaba to any other bus station in Amman, since you'll just be adding more time and effort to your journey to reach Mujemma Al-Janoob.