So from what I can find, Rucker is in the Chiricahua Mountains north of Douglas. First off MTB Project has some miss leading info on the AZT, they are showing the hiking trail in wilderness. Go to the AZT page in the routes section of this site to see options for riding the AZT south from Tucson. Or just take the race track from the AZT750
http://topofusion.com/azt/race.phpIf you look at the AZT network from this site at the south end you will see a bike terminus, and the not open to bikes trail from Montazuma Pass to the official start of the AZT.
So to get to Rucker you need to go quite a ways East. And obviously you don't want to take the I-10 freeway. Theoretically you could take the AZT all the way to near the border and then head east over Montazuma Pass thru the Monument and then on the highways towards Bisbee then to Douglas and then back north. Could this be done in 4 days I guess that depends on your pace.
More realistically. You could leave the AZT course at Sonoita and head east on highway 82 to highway 80 to Tombstone. From there go east on the Gleeson road. Then your going to get to Elfrida some maps label this highway 666 some 191. Then it looks like you need to go north from Elfrida to be able to go east up Rucker Canyon.
Hope this helps.
Tim