Greetings,
Me and my friend are going next year on a motorcycling trip from Croatia to Jordan, and are currently in phase of creating a plan for the sponsors (hence my early inquiry). Basically, everything has been going smooth so far until we got to the middle eastern part of the map, and the most important part of our trip. Our plan was to go - Turkey, to Syria, Lebanon, Israel over to Jordan and go back on a slightly different route, probably Jordan directly to Syria and back to our starting destination. As we see it now, we have two big problems there and that's the current deteriorating state of affairs in the region and our visit to Israel.

First issue is out of our influence and we just have to wait until mid September of 2014 to see how it will play out.
The second one is a lot more tangible and needs to be solved before we head on in further planning. After exhausting search in the abyss of the internet, I've only found one option that will require us to change our route slightly to Syria, Lebanon, back to south Syria, Jordan and then cross the King Hussein/Allenby Bridge into Israel (purportedly Jordanians don't stamp at exit there) and then back through Jordan and Syria. That should leave us without any evidence of being in Israel. But now it appears, from some old and scarce bits of information, that Allenby bridge is a specific type of border crossing where people board special shuttle buses to pass it.
Does anyone know if there's a possibility of crossing the bridge with a bike, or if there is any other way of visiting Israel and managing to go back through Syria/Lebanon?

There is an option of leaving the bike in Jordan and visiting Israel bike-less, and then going back normally through Syria and/or Lebanon from Jordan, but you guys understand why I would try any other option over that (unless it's the only option).

Thank you,
Marko