Jeanine Moss never expected to get into the cannabis industry. But that was before her hip-replacement surgery.

Ms. Moss, 62, of Marina del Rey, Calif., had quit her job as a marketing consultant before she had her hip done in 2014. As she left the hospital, her doctors handed her a “shopping bag filled with opiates,” she said. The drugs made her disoriented and woozy.

So she switched to medical marijuana, which is legal in California and was familiar to her, having grown up in the nearby Venice section of Los Angeles. Within a week, she had tossed away her pharmaceuticals.

As it turned out, Ms. Moss was in good company: Many of her friends were also using cannabis to manage their ailments. Slightly embarrassed about carrying around a drug associated with naughty high school students, the older women would lament that they had nowhere to stash their drugs.