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.
WRU International Skills Coach Jason Strange is a busy man, combining the new role with that of Wales Under 20 attack coach, Ebbw Vale head coach and continuing to teach at Ebbw Fawr Learning Community.
Warren Gatland and Sam Warburton look ahead to this week's crunch RBS 6 Nations tie against France, where the Wales skipper in particular is keen to make his mark, as Paris has proved a bleak place for him in the past.
Following their historic win over England, Wales Under 20 suffered a narrow, 36-34 loss to their Scottish counterparts last weekend, despite outscoring them by five tries to three. Watch the match highlights and reaction.
WRU TV go behind the scenes with the Wales squad as they put the final touches in place ahead of the clash against Scotland at Murrayfield. Follow the squad on their captain's run, the kickers visit to Murrayfield and Neil Jenkins' press conference