Another Indian Shiv Kapur however was struggling at two-over through 12 holes.
Bhullar, who has made good starts in the past few weeks, has been unable to hold on to them, but has nevertheless been steady in his rookie season on the European Tour.
Bhullar was three behind the early leader, American Connor Arendell, who birdied four of his last five holes to snatch the clubhouse lead.
He birdied the 10th to get to two-under but slumped with a double bogey on par-3 12th. He quickly recovered with four birdies in last six holes, two on last two holes.
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Bhullar said,"I had 15 greens in regulations, which is very good on this kind of a golf course, which is up and down. My short was also up to the mark and I also made a good sand save."
He added,"This is my first time in this beautiful golf course. It also reminds me of some of the old-school golf courses in India, where the ball tends to run a bit and it can be tricky.
Bhullar, who is a key member of the Asian Team for EurAsia Cup later this month.
"I am looking forward to EurAsia Cup and I have been touch with some of the members and it will be great to get there."
India's Anirban Lahiri will also be part of the Asian team, lead by Thongchai Jaidee.