In what was a clumsy start, Ulster conceded a penalty in the opening passage of play and were quickly made to pay when Coetzee finished off a maul try after only two minutes.
Turned over when given the opportunity to respond in kind, Ulster were soon defending their own line again but it took until the 19th minute for the Bulls to double their advantage, the hosts opting for the quick-tap when five metres out to set up an infield maul with Elrigh Louw dotting down.
With both the altitude and the bruising nature of the contest taking its toll on Ulster, Coetzee was over for his second and his side’s third with a pick-and-go from close range eight minutes before the interval.
Seemingly hanging on and no more in the contest, Ulster scored their first points of the half with the clock in the red after working the ball well through the hands to send the speedy Chay Mullins over in the corner for his second try of the season.
Despite an uneven start to the campaign that now comprises of two draws and two losses in the league, spirited second halves have been a story of Ulster’s season and they again were much brighter after the restart.
Mike Lowry thought he was over only to run out of room in the left corner but flanker David McCann barged across soon after.
Having been rocking on their heels in the first half, Jack Murphy’s second conversion of the day left just seven points in it and Ulster’s prospects improved further with Coetzee sent to the sin-bin after being shown a yellow card that stayed yellow when reviewed by the TMO bunker for a high hit.
By the time the former Springbok returned, it was his side who had scored the only points of his absence through a Handre Pollard penalty.
It was a further 10 minutes after the Bulls’ captain’s reintroduction before the game’s next score with Keynan Knox doing well to create space for his team-mates to send Mullins over for his second.
Deflatingly for the visitors, virtually from the restart Johan Grobbelaar scored yet another forwards’ try for the Bulls.
Stuart McCloskey, one of eight Ulster players who featured now joining up with Ireland for the Nations Championship, set up a grandstand finish with his side’s fourth try 10 minutes from time.
They could not, however, close the gap in the final stages before Bosch’s concluding penalty cost them a further point.
