Jeev had four birdies against three bogeys, while Bhullar, who is playing his rookie year on European Tour, also had two birdies and one bogey.
England's Eddie Pepperell was the sole leader on a tightly packed leaderboard with a round of 68.
Pepperell carded an opening four under par 68 at PGA Catalunya Resort to finish a shot ahead of a group of eight players, including pre-tournament favourite Sergio Garcia and fellow Spaniards Miguel Angel Jimenez and Rafael Cabrera-Bello.
Garcia had enjoyed the calmer morning conditions as he set about justifying his billing as pre-tournament favourite with an opening 69.
Fresh from his third place in the Players Championship at Sawgrass on Sunday, Garcia shrugged off a bad night's sleep as he looks to win his national open for the second time, 12 years after his previous success.
The World number seven carded three birdies, an eagle and two bogeys.
