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.
Ebbw Vale captain Damien Hudd picked up the biggest accolade of the night at the 11th Principality Premiership Awards Evening held at Principality Stadium, after leading his side to the title for the first time.
Wales assistant coach Robin McBryde is predicting a tough battle against England on Sunday despite the fact they may not be considered to be at full strength. Players will be out to impress Eddie Jones which makes England a dangerous proposition, he says.
Wales U20 captain Tom Phillips and performance psychologist Dr Rich Neil explain why spending three days at Monmouth RFC has further strengthened the togetherness of the squad ahead of the #WorldRugbyU20s
Alongside Scarlets flanker James Davies and Cardiff Blues centre Cory Allen, three Wales Sevens core players have made the extended training squad for GB Sevens. Wales Head coach Gareth Williams tells WRU TV's Graeme Gillespie why Luke Treharne, Sam Cross and Luke Morgan earned selection in the initial training squad for Rio.