Ulster responded with a try of their own a few minutes later when Jacob Stockdale crossed over after the Bulls defence was caught napping and Nathan Doak was on point from the kicking tee.
The Bulls pulled away with David Kriel’s try after 13 minutes and when the imposing Grobbelaar powered home after a forceful driving maul shortly before the half time break.
The Bulls tightened their grip on the match two minutes after the break when Springbok winger Moodie evaded tackles from Ulster players before touching down for their fourth try of the afternoon.
Bulls continued to pile more pressure on Ulster, who only came alive in the late stages of the match, and they were duly rewarded after 55 minutes when Cameron Hanekom added his name on the scoreboard.
The Bulls had time for another try and this time it was Chamberlain, who ended his day with eleven points, to put his name on the scoreboard as the home side took full control of the match.
After this, the Bulls have four weeks on tour in Europe where they are scheduled to play against Ospreys, Scarlets, Benetton and Connacht as the campaign will be gaining momentum.
Ben Carson and Stewart Moore scored their two late consolation tries but Louw scored the last one three minutes from the hooter as the Bulls earned a deserved home victory.
In the other URC played earlier on Saturday at Ellis Park, Rabz Maxwane scored three of the eight tries by the Lions as they thrashed Edinburgh 55-21 to move into the top half of the table and David Kriel converted.
Scorers
Bulls (21) 47 Tries: Kurt-Lee Arendse, David Kriel, Johan Grobbelaar, Canaan Moodie, Cameron Hanekom, Boeta Chamberlain, Elrigh Louw Conversions: Boeta Chamberlain (3), David Kriel (2), Keagan Johannes (1)
Ulster (7) 21 Tries: Jacob Stockdale, Ben Carson Conversions: Nathan Doak, James Humphries (2)