When I traveled from Jerusalem to Jordan, via the Alleby/King Hussein bridge, I did much the same as you plan. I did not find this border crossing to be nearly as challenging as a lot of people report.
The short version of my experience was as follows: We arrived just as the crossing opened. There were five busloads of Iraeli Arabs traveling to make umrah in Makkah. The politics of the situation was a bit confusing, but as it was reported back to me and other travelers in a combination of broken English and broken Arabic, they were processed first because they were Israeli citizens. (I had thought that Israelis could not use this crossing, but perhaps that restriction does not pertain to Arab citizens of Israel.) In any event, I offer the details just to illustrate that the crossing is more efficient than its reputation would indicate.
With the five busloads ahead of us, many frequent travelers that were waiting with me said this was the worst they had ever seen, and they expected long delays. One person was convinced she would miss a flight because of it. So we were delayed for about 45 minutes getting to the departure hall. But when we got there, all five busloads had already been sent on to Jordan, and it was smooth sailing. There's a lot of standing in line and waiting for a bus, or a passport check, or whatever. But we were released into Jordan by 10:30 AM. I had a rental car waiting for me, and headed south rather than east – but I suspect you could be in Amman by 12:30 in most cases.
Because my own trip preparation had involved reading and posting a lot of questions (and finding few answers) about what exactly to expect at the crossing, I gave into an OCD compulsion and documented it step-by-step. In case this is helpful to you, I will re-post it here:
(1) Arrive at the first checkpoint.
(2) Wait in line to approach the checkpoint.
(3) Show your passport to enter the Allenby Bridge area.
(4) Receive a ticket (the driver in our case, not us) allowing approach to the terminal.
(5) Arrive at the second checkpoint (about 2 km).
(6) Wait in line to approach the checkpoint.
(7) Present the ticket received at the first checkpoint.
(8) Approach the terminal (about 200 m).
(9) Give the luggage to an employee, who puts it aside.
(10) Walk through an open-air metal detector to approach the terminal and enter the Departures Hall.
(11) Pay (all simultaneously) the Israeli exit tax, the luggage fee, and the bus transport fee.
(12) Go through passport control and show the exit tax receipt.
(13) Exit the building
(14) Point to nearby waiting luggage so it can be placed on a Jordan Express Tourist Transport (JETT) bus.
(15) Wait for the bus driver to get departure approval from the Israeli authorities.
(16) Ride over the bridge.
(17) Arrive at a stop on the Jordanian side (about 2 km)
(18) Relinquish passport to a guard, who reviews it and and hands it to the bus driver for safekeeping.
(19) Arrive at the Jordanian terminal (about 3 km).
(20) Exit the bus and walk into the terminal
(21) Wait for luggage to be unloaded from the bus.
(22) Approach the scanner as your luggage is being placed through it by the Jordanian authorities.
(23) Retrieve luggage after scanning.
(24) Walk (with luggage) to the right of two side-by-side windows (because Arabic is read right-to-left, this is probably intuitive to the Jordanians, but it felt backward to us – more so because we were approaching the windows from the left).
(25) Identify the passport by nationality and name.
(26) Wait while the employee visually confirms your identity.
(27) Wait while the passport is passed, behind the glass, to the left of the side-by-side windows
(28) Wait while the passport is processed.
(29) Listen for your name to be called at the left window.
(30) Retrieve the passport.
(31) Enter the Hashemite Kingdom of Jordan.
I hope you have a fantastic time in both of these wonderful countries.
-- Joe / Atlanta / USA