Bhullar, who shot an even par 72 in first round, added a four-under 68 aided by four successive birdies from eighth to 11th holes, two birdies on either side of the turn. He earlier birdied the third but dropped a shot on seventh.
Jeev Milkha Singh (69-75) and Shiv Kapur (71 and one-under through 13 holes) are also likely to make the cut.
Jeev Milkha Singh, who opened with a three-under 69, had a tough day with a three-over 75 which included three bogeys in a span of five holes from fifth to ninth holes.
Jeev will have to wait for the round to finish to see if he makes the cut, as he lies tied 59th, and the cut looks likely at even par, which is where Jeev is currently.
Rafael Cabrera-Bello (67-67) was in the lead at 10-under, while Lee Craig (68-67) is second at nine-under.
Danny Willett was on fire with nine-under 63 and moved to third at eight-under following his one-over 73 on first day.