There is Cycling Jordan. It organizes weekly cycling trips around the Jordan Valley/Madaba Governate/Dibeen Forest/Wadi Rum. There are usually many foreigners there as well as Jordanians. Most of them are pretty active and stuff, so if you talk to them, I am pretty sure they know more stuff like that.
Their website:
Hope it helped 
I emailed Cycling Jordan about upcoming events but they haven't seemed to reply or send out any updates. Reading your post reminded me to check their site, and I guess they had a ride last weekend. I totally would have gone had they sent anything out, but what can you do. If I see any updates on their site about activities I'll post them here.
Has anyone been on one their rides?
Also just noticed they have an rss feed on their blog, so subscribe to that if you want updates.