The Bulls have to travel to Pontypridd, but will be full of confidence after they beat Division front-runners Bonymaen 26-22 at the weekend, courtesy of six goals from outside-half Rob Lloyd.
Team manager Justin Lewis said the hard-earned victory was perfect preparation for the trip to Sardis Road.
"We were 19-0 down after only 10 minutes, but we had chosen to play into the wind in the first half and that paid off," he said.
"It wasn't a day for the backs, so in the second half, we knew we had to keep it in the forwards and keep driving it up the middle. We've missed Rob Lloyd for the last three games, because he's a Marine and he's been away, and his kicking was crucial.
"We said before the game that we could win this one, and we knew it would give us a lot of confidence ahead of playing a Premiership side at Sardis Road.
"This season is strange - we can produce this sort of performance against the good sides, but can't seem to do it against the poorer sides."
In the other quarter-finals, Cardiff host Llandovery at the Arms Park, Maesteg take on Newport and Swansea welcome neighbours Neath to St Helen's.
Cardiff are staring Premiership relegation in the face, but will fancy their chances against the Drovers, who are only three points ahead on the table, having played one more game.
The two sides have met twice in the League this season, with results going to the home side. Cardiff won 21-13 in October, with Llandovery avenging that result with a thrilling come-from-behind 39-31 victory at the end of January.
Newport beat Maesteg 23-14 at Rodney Parade in October, but they will have to be on top of their game for the away trip this weekend.
Premiership table-toppers Neath will be favourites in their match against Swansea, having beaten the All Whites 17-6 in dire conditions last weekend. The last time Neath travelled to St Helens - in November - they came out on top 39-3.
Wales Head Coach Rob Howley talks to WRU TV's Sebastian Barrett about the 36-man squad he has just named for the forthcoming Under Armour series, which includes two uncapped players, Ospreys duo Sam Davies and Rory Thornton.
Head coach Rowland Phillips is deligthed he can now call BT Sport Cardiff Arms Park home for his Wales Women's side, who launch their international season next month with games against Scotland and UK Armed Forces in the heart of the capital city.
Wales Sevens star Sam Cross has put his home town club of Brynmawr on the map after winning a silver medal at the Rio Olympics with Team GB. His club have now honoured him by naming their players bar after him, as WRU TV discovered at the official launch, recently.
One of the newest members of the Principality Premiership, Bargoed admit it's proving to be a steep learning curve at the highest level, but are determined to become a force to be reckoned with. WRU TV visited the club last weekend when they took on Llanelli.
Table-topping Aberavon travel to north Wales to tackle RGC 1404 as both teams defend unbeaten starts to the season in the Principality Premiership. WRU TV's Graeme Gillespie visited the Wizards to see how their preparations were going for the game of the weekend.
The Half a Game initiative is currently sweeping across Wales and proving a major success. The scheme aims to give every young player at least half a game every weekend. WRU TV recently visited a festival in Narberth where clubs have fully embraced the initiative.
Both Bargoed and Swansea were seeking their first win of the Principality Premiership season this afternoon. It proved a fruitful day for the hosts - not only did they win, but Bargoed claimed a try bonus point.
Cardiff managed to keep their unbeaten record at home intact, but only just as Bridgend made them work extremely hard before the Blue and Blacks secured a hard fought Principality Premiership win at the BT Sport Arms Park last night.
Former Wales back row Andy Powell gives a guided tour of The Wern, home of Merthyr RFC, who are determined to prove a lot of people wrong and make their mark in their first season in the Principality Premiership.
Wales Sevens head coach Gareth Williams looks back on the Rio Sevens success where he helped GB win silver. He believes the successful campaign is a huge boost to his Welsh squad as they prepare for another World Series, as WRU TV's Graeme Gillespie discovers