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 Under 20 travel to Newcastle on Friday to face England at Kingston Park. With the likes of Jack Dixon and Ashley Evans returning to the squad, it's arguably the strongest side head coach Byron Hayward has put out in the tournament so far. WRU TV previews the game with Defence Coach Richard Hodges and captain Steffan Hughes.
Wales head coach Warren Gatland gives an exclusive interview to WRU TV after naming his side to face England in the RBS 6 Nations at Twickenham on Sunday. Gatland has recalled British & Irish Lions duo Jonathan Davies and Alun Wyn Jones to his side while Rhys Webb retains his place at scrum half.
Scrum half Rhys Webb and lock Jake Ball both made their first Wales starts in last Friday's win over France at the Millennium Stadium. They talk exclusively to WRU TV's Luke Broadley about their experiences of the day.
Wales Women's Head Coach Rhys Edwards has made three changes to his side to face France at Aberavon on Sunday, where he expects his side to be given a tough time against one of the best teams in the world.