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.
Roger Lewis talks to WRU TV at the announcement of a new £60 million Rugby Services Agreement (RSA) which provides a new and positive contractual relationship between the WRU and its four Regions for the next six years has been agreed.
The Welsh Rugby Union has announced a major new sponsorship deal with Gullivers Sports Travel which will make the UK's leading, and longest established, multi-sport tour operator, an Official Supplier for the rest of the decade.
Having taken part in seven World Cups as a player and coach, Liza Burgess hopes to go out in style this afternoon when Wales take on Australia in the Play-off for seventh and eighth place in the Women's Rugby World Cup in Paris.
WRU Head of Rugby Josh Lewsey met with volunteers across the game earlier this week, championing their role in the sport. He was joined by Wales captain Sam Warburton for part of the day as volunteers took part in a 'Try Out' event for the 2015 Rugby World Cup
Wales Women may not have got the results they wanted recently on the field, but off it they have made massive strides in strength and conditioning - and that is in no small part due to S&C coach Sam Dodge.
Two weeks into the new pitch project at Millennium Stadium, Groundman Craig Campbell takes staff on a unique behind-the-scene tour of the works so far and National Squad Assistant Strength and Conditioning Coach John Ashby and Tour Guide Peter Owen describe what the revamp means for them.
Try-scorer Jenny Davies and fellow prop Megan York reveal to WRU TV's Graeme Gillespie their thoughts after Wales broke their drought in the Women's Rugby World Cup with a 35-3 win over South Africa in Paris.