We found the bus services to be fine, both to and from Amman,
We used the Bus to get from Jerash to Amman thensouth to Karak, at the beginning of our trip.
Then again at the end to get the bus from Madaba to Amman.
I think the bus station in the photo is Zacara
The bus to city centre leaves every 30 min,the ticket costs 3JD and is about 50 to 1 hour by bus (mini yellow bus).
The bus is located just front of exit.
Amman City Tour has been lunched, details and route here: