After a bear climbed through the bathroom window and trashed his family’s cabin in the Sierra, Eric Persha had every reason to resent the opportunistic omnivores, who will eat just about anything they can get their paws on. But when he and his family discovered a black bear on his in-laws’ property near Bolinas in June, they were happy to make its acquaintance—if only via webcam.

“We’re excited about it,” Mr. Persha said. “It’s a…