The court heard Mulligan, 64, admitted to being behind the wheel of his Hyundai Getz when it collided with the 54-year-old cyclist on Belmont Road at Kenwick about 6pm on Friday.
Mulligan allegedly did not leave his vehicle, waiting several seconds then driving off.
Residents found the injured cyclist on the ground and called emergency services, who rushed him to Royal Perth Hospital with life-threatening head injuries.
He remained there tonight in a critical condition.
Police arrested Mulligan yesterday and seized his car, charging him with failing to stop and ensure assistance, and failing to report the collision.
A magistrate today told the truck driver the charges he was facing were “very serious”, advising him they might be upgraded as police were unsure whether the cyclist would survive his injuries
Mulligan was granted bail with several restrictions but prosecutors did not ask for him to be suspended from driving, allowing him to keep working.