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 Welsh Rugby Union is forming a new Youth Board with a brief to help keep more young people involved in the game during their late teenage years and beyond. The first task of the fifteen strong Board will be to analyse and consider the issues which lead to a number of youngsters drifting away from the sport between the ages of 16 and 21. To apply visit www.wru.wales/youthboard
The Foster's Challenge Cup will involve the 12 Principality Premiership sides and will run during European and British & Irish Cup weeks, providing vital fixtures for the participating clubs and an opportunity for upcoming players to step up to semi-professional rugby and make a claim for starting places within the Premiership squads.
Eighty schools and colleges in Wales now have a full time rugby officer as part of the WRU's school club hub scheme. All of the school club hub officers recently gathered at the National Centre of Excellence for various workshops.
With Liam Williams forced out of the World Cup through injury, lock Luke Charteris and Skills Coach Neil Jenkins say they have to put yesterday's defeat behind them as Wales now look ahead to another physical encounter against South Africa in the quarter-finals of the Rugby World Cup.
WRU Consultant Head of Physical Performance Paul Stridgeon praises the Physical Performance department for their work and dedication as he addresses the media ahead of Wales' Pool A clash against Australia
Twelve young people have been selected to follow a one year WRU Coach Core apprenticeship programme. Coach Core was set up by the Royal Foundation of the Duke and Duchess of Cambridge and Prince Harry as part of the Olympics legacy in 2012 and the Duke of Cambridge was on hand to meet the apprentices on their first day in the job. The programme has been funded by the Hunter Foundation.
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'.