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.
The WRU has launched a campaign to create a long term legacy for Welsh club rugby by highlighting the advantages of volunteering. Rhian Edwards, a volunteer at Seven Sisters, has enjoyed many benefits of her volunteering at a grassroots rugby club including being part of the Rugby World Cup volunteer workforce after being nominated by the WRU - and the WRU is asking for more people to develop their 'Welsh rugby roots'.
Wales head coach Warren Gatland and captain Sam Warburton say their first prioirty on Sunday in the opening game of the World Cup is to win against Uruguay and not get overly concerned with points difference.
With only days to go until the biggest rugby competition in the world begins, rugby fans visiting Cardiff this autumn will be able to enjoy a special display at National Museum Cardiff as part of the celebrations surrounding the Rugby World Cup.
Geraint John has taken up the new role of WRU elite coach development manager having arrived in Wales last week. WRU TV caught up with him at the WRU rugby department's strategy day at the Millennium Stadium.
The entire Welsh Rugby Union Rugby Department gathered at the Millennium Stadium earlier this week where WRU Head of Rugby Josh Lewsey looked back on a year where structural and strategic changes have seen significant progress made
The Welsh Rugby Union has released a specially produced video to spearhead a new campaign to help promote the values of rugby union. The video, entitled Let us Play underpins the WRU rugby department's philosophy - to engage, transfer and retain players, coaches and referees.