Unscrew light bulbs from your lamps. Place incandescent light bulbs in one paper bag and fluorescent light bulbs in the other. Place each paper bag in a plastic bag and tie the plastic bag to secure it. As Aircycle notes, the state of Arizona prefers to recycle fluorescent bulbs and in fact requires it in many communities.
Call your town's trash collection program to check on rules for your Arizona community. Light-bulb disposal is regulated at the city and town level, not the state level. For example, Tucson requires residents to bring fluorescent bulbs to a hazardous waste center. Flagstaff allows residents to throw out double-bagged incandescent bulbs, but mandates fluorescent bulbs go to a hazardous waste facility.
Throw out the bag of incandescent bulbs in your garbage bin, if this is your town's policy. Since the bulbs are in a paper bag and a plastic bag, they're double-bagged.
Bring fluorescent light bulbs to a hazardous waste facility if this is your town's policy (as for Flagstaff and Tucson). If you can throw away fluorescent bulbs in your town, do this.
Take fluorescent bulbs to a Home Depot location near you, if this is more convenient than visiting the waste facility. As the cities of Tuscon and Flagstaff both note, local Home Depot stores accept old fluorescent light bulbs at the store and will recycle them for you.