I did some research for you. There is little to no BLM land east of Tucson along the I-10 corridor. It is primarily a combination of Arizona State Trust land and private property.
Here's a link which shows you a macro view of property ownership:
Ownership mapOf course, you'll need a property owner's permission to camp on their property.
To camp on AZ state trust land, you'll need to obtain a permit. I'm providing a link here for the permit application site. A family permit ($20) will allow for two adults and any children under 18 years of age. You are limited to 14 days of camping per year with your family permit.
Arizona State Trust Use Permit ApplicationI hope this is helpful.
Jim
2016 Ford F350 Turbo Diesel SRW 4x4
2017 Grand Design Reflection 297RSTS
2013 Ford F350 Turbo Diesel SRW 4x4 (Destroyed by fire - 8/29/16)
2014 Grand Design Reflection 337RLS (Destroyed by fire - 8/29/16)