The most convenient public transportation in Jordan is the Jett Bus. Originally designed as tourist infrastructure, it actually moves a lot of locals around, especially on the Aqaba to Amman route. Technically the Jett bus is the only organized form of public transit in the country so while I say it is conveninet, it is really your only offical choice.
There are other busses, mini busses, that operate all over Jordan. However, they do not have any schedueld departures and take cash fares. If you want to be able to book your bus transportation in Jordan in advance, then you will want to do it online.
The Jett Bus is just one of the many ways to get around Jordan. I have written many transportation guides to help you navigate your way around the country. Click below on how best to get around Jordan by Jett Bus.