Play-off chasing Cardiff came tantalisingly close to a priceless bonus point as they staged a late rally at Loftus Versfeld.
But it wasn’t to be in the end and they came away empty handed against a highly impressive Bulls outfit.
The South African hosts dominated the opening hour and ran in five tries in all, with their wing Sebastian De Klerk crossing twice.
However, Cardiff struck twice late on, as lock Teddy Williams and eye-catching wing Gabriel Hamer-Webb added to an earlier score from flanker Alex Mann.
That left them just one try short of a bonus and they threw everything into attack in the dying minutes, only to just run out of time.
So they must now wait on other results to see what they will need from their final regular season game against the Stormers in Cape Town next Friday night in order to make the URC play-offs.
They had made six changes in personnel from the side which secured a thrilling 26-21 victory over Munster at the Arms Park a fortnight ago.
Tinus de Beer came in for just his fifth start of the season at No 10 to form an all South African half-back partnership with Johan Mulder. It was a big day for the pair as they were both playing in their home city of Pretoria.
The other changes were all in the pack, with Rory Thornton making a rare start at lock, Corey Domachowski and Evan Lloyd stepping in at loosehead prop and hooker respectively, while Mann and Alun Lawrence were brought into the back row.
With hooker Liam Belcher kept in reserve on the bench, centre Ben Thomas took on the captaincy.
As for the Bulls, they fielded a star-studded line-up including the likes of Springboks Willie le Roux, Canan Moodie, Wilco Louw, Marcell Coetzee, Ruan Nortje and Cameron Hanekom.
With play-off rivals Munster having claimed a 38-20 bonus point victory over Ulster on Friday night, Cardiff went into the game in sixth place in the table, level on points with the Irish province, but behind them on points difference.
When the contest got underway in warm sunshine, it soon became clear just what a challenging assignment this was going to be for Matt Sherratt’s team.
After swiftly opening the scoring through the boot of fly-half Johan Goosen following a scrum penalty, the hosts claimed their first try in the seventh minute.
Hooker Johann Grobbelaar delivered the key offload out of the side door, with centre Harold Vorster then winning the race to Moodie’s chip over the top.
Winger Moodie was also heavily involved in the build up to his team’s second try, making good ground out on the right.
Then when the ball was moved back right, prop Wilco Louw powered over after his skipper Nortje had been brought down just short of the line.
Having helped pave the way for the first two touchdowns, Moodie then got in in the scoring act himself, racing over after classy full-back Willie le Roux had pounced on a deflection from an aerial contest.
The Bulls continued to dominate the first half in terms of possession and territory, taking a firm grip on proceedings.
Their sustained pressure was again rewarded a minute before the break as they secured their bonus point fourth try.
With Irish referee Eoghan Cross playing advantage for a scrum offence, No 8 Hanekom picked up from the base and surged across the whitewash.
Replacement fly-half Keagan Johannes, who had come on for the injured Goosen, added the conversion to make it 31-0 at the interval.
The hosts extended their lead soon after the resumption with winger Sebastian de Klerk sprinting in after collecting an intelligent kick over the top from the classy Le Roux.
But there was finally some cheer for Cardiff a few minutes later with a well taken try from flanker Mann.
Off an attacking lineout, Hamer-Webb produced a strong carry in midfield before substitute centre Rory Jennings fed Mann with a long pass.
The blindside had plenty of work to do, but did it well, squeezing in at the left corner despite the attentions of two defenders.
Thomas, who was now playing at fly-half with De Beer having been replaced by Jennings at the break amid a reshuffle, slotted the touchline conversion.
Back came the Bulls with a second score for Le Clerk who showed good pace and strength to reach the line after another assist from Le Roux.
Cardiff threatened a second try of their own when Hamer-Webb sliced through out on the left but Cam Winnett was unable to hold on to the scoring pass.
However, with their bench – notably Taulupe Faletau, Teddy Williams and Dan Thomas – making an impact in the final quarter, they managed to conjure up two tries in the closing stages.
After replacement Dan Thomas broke away from a lineout maul, his fellow flanker Mann spun out of contact and sent replacement lock Williams over, with Ben Thomas converting.
Williams then played his part in the build up to the next score, breaking through in midfield ahead of flanker Dan Thomas delivering a miss pass which enabled the impressive Hamer-Webb to dive in at the corner, with Ben Thomas again converting from wide out.
Cardiff then went in search of an all-important fourth try as they tried everything they knew in the final play but the clock just beat them.