He has a four-shot lead over fellow American Denny McCarthy, who fired a five-under 67, while Brendon Todd trails Bhatia by seven shots.
Japan’s Hideki Matsuyama moved into contention with a bogey-free round of 66, which featured six birdies, putting the 2021 Masters champion eight shots off the lead at seven under.
McIlroy, who is playing in his final tournament before The Masters next week, and Ryder Cup team-mate Tommy Fleetwood both had a frustrating day on Saturday – the Englishman also went round level par in San Antonio.