I know a few pro winemakers as I'm just lucky and live an hour south of Napa/Sonoma. My understanding is that the biggest question is educated via school (UCD obviously the biggest/best known program) vs. learned on the job. So if you already have on the job training, then probably simply adding a UCD certificate would be more than enough. But if you are trying to get into the industry with no pro experience, then the bachelors makes more sense. Especially if you haven't been to college and are interested in it (UCD is a great school, not just for wine makers).
Most of my winemaker friends fell into it via parents, spouses, homewinemaking, friends, getting a winery job, but one was a pro. chef trained at the CIA in NY worked at great restaurants for over 10 years, then took community college science classes in order to qualify to go to UCD for winemaking. She's now been doing winemaking for 20+ years, it got her in where she did not have an in, but she's the exception of the folks I know. But many of the others won the genetic lottery or had other connections.