Lots of options starting with the Arizona Trail near Colossal Cave.
Starting off of Pistol Hill road a main access point
http://www.sdmb.org/trails/AZTrail-Pistol-Hill and riding south bound. The trail is mostly easy until you get to the Forest boundary then it starts getting tough.
You can always take hwy 83 south to Gardner Canyon road and then head west into the mountains. Then you could work on riding more of the trail on the way back. It's never going to be all down hill but its less climbing on the way back north.
Hasn't rained in a while so the only water source may be at Kentucky Camp (spigot) or possibly Gardner Canyon itself may be running there should still be snow melting. But if you don't have a water filter or some way to purify best to stick to the spigot.
You might also consider just doing a Sub 24 hour overnighter just to get your feet wet. This could easily be done on the AZT near Pistol Hill.
Assuming you have been mountain biking for a while at least. Assuming you have some car camping and other outdoor experience. Assuming you'll be attempting to bikepack with heavy car camping type gear.
That's a lot of assumptions on my part. Its totally possible to get out there using what ever kit you have. But it's hard to cover much ground with heavy gear. Thus the idea of a shorter first time out.
If that works out for you give a 2 day one night run a shot with a little planning it can be a lot of fun. Or you may find yourself calling someone for a ride home when you run out of water and find yourself hurting.
Last summer a guy had to call in search and rescue when he got in over his head on the north end of the Catalina's.
Not trying to dissuade you in any way bikepacking is great fun once you get all of the bugs worked out.
I have learned a lot over the years and made a lot of mistakes. some of them more then once. I would be more then willing to answer and questions you have.
Tim
Welcome to Bikepacking the most fun you can have on 2 wheels.
