Bhullar, who had a superb 67 on first day, has a two-day total of seven-under and was tied for 29th after 36 holes.
Meanwhile, Jeev Milkha Singh (71-70) and Anirban Lahiri (68-73) missed the cut by a shot with a total of three-under 141. Also missing the cut was Shiv Kapur (73-69).
Four players share the halfway lead heading into the weekend. Rafa Cabera-Bello and Pablo Larrazabal, flying the Spanish flag on the day the movie "Seve" hit the big screens, were joined on 12 under par by 2012 BMW International Open Champion Danny Willett and Argentina's Emiliano Grillo.
Larrazabal made the greatest gain with a nine-under 63 to reach 12-under 132, a 36-hole total matched by Grillo with a 66, and the two overnight leaders Cabrera-Bello and Willett who shot matching 68s.
The cut fell at four-under, just one short of the lowest of the European Tour season.