Tiger Woods used to enjoy going to topless bars, but he always pretended he was a wide-eyed innocent who’d never seen a stripper before, sources say.

Before his fateful Thanksgiving car crash, Woods made regular trips to Scores whenever he was in town, according to the mammary mecca’s former manager, Tony Lombardi. The golf great was able to appear like a shy “virgin to strip clubs,” Lombardi said.

Woods’ acting talent came to light as Page Six investigated how the billionaire had been able to conceal for so long his very energetic extramarital activities. It turns out he had a phalanx of handlers to pre- vent incriminating photos from being taken.

Tiger’s protectors include his gruff caddy, Steve Williams, a hulking New Zealander. His agent at IMG, Mark Steinberg, helped kill a National Enquirer story about his alleged romps with pancake-house hostess Mindy Lawson by offering Woods as a cover to sister publication Men’s Fitness.

While out on the town, Woods was careful not to approach any potential conquests himself, preferring to let a member of his entourage make the introduction. “There are always a lot of other people around, so it’s never one on one — it all looked very normal,” night-life impresario Rocco Ancarola told The Post’s Brad Hamilton.

“It camouflages what’s going on. He’d just point and say, ‘Who’s that?’ and they’d go over and say, ‘Tiger Woods wants to meet you.’ And they would never leave together.”

Ancarola, who later hired Woods’ mistress Rachel Uchitel to lure VIPs to his Pink Elephant club, said Tiger benefited from an industrywide reluctance to whisper about wealthy customers — an omerta policy Ancarola plans for his new restaurant, Rabbit in the Moon, in the West Village.

“We in the business do that without thinking about it,” he said. “You tend to protect the celebrities.”