According to Bernalillo County Planning and Development Services' homeowner permit guide, flatwork such as walkways and driveways doesn't require a building permit, and neither does a shed under 120 square feet. A detached structure over 120 square feet does, and permits and applications are valid for 180 days. The County's building inspectors can be reached at (505) 314-0351.
Where the driveway meets the road is a different matter. Bernalillo County's draft Technical Standards call for a driveway permit from County Public Works for new or modified connections to a County road, and for paving of 1,000 square feet or more. The same draft sets residential driveway widths at a 12-foot minimum, 14 feet preferred and 22 feet maximum, and requires contractors working in County right-of-way to be licensed, bonded, insured and approved. Because that document is a draft, we confirm the current rule with the County before work in the right-of-way.