Winner of the Fiji International last year, Bhullar trailed the leader, South African Louis de Jager, who opened up a commanding four-shot lead at the halfway stage.
De Jaeger carded a second round of 66.
Other Indians making the cut were S Chikkarangappa (70-69) in tied 15th and Khalin Joshi (72-69) in tied 33rd place, while Shubhankar Sharma's lean patch continued with a missed cut after rounds of 74 and 71.
The South African shared the overnight lead with England's Jack Singh Brar going into day two, but after seven birdies in the second round he opened up a big lead.
Four shots off the pace in a share of second place were Brar and Spaniard Adri Arnaus, both of whom are European Challenge Tour graduates.
Also, in contention again was South African Justin Harding, who was five behind his countryman de Jager. The world number 52, who triumphed in Qatar last week, is looking to become the first player to win back-to-back European Tour events since Justin Rose, who achieved the feat in 2017.
A good finish would also bring him inside Top-50 and earn him a place at the Masters.
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