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.
As the countdown continues for RWC2015, Tournament Chief Executive Debbie Jevans visited the Millennium Stadium to discuss preparations for the eight matches and reveal the positive news that 100,000 tickets for games at the home of Welsh rugby have sold in the last seven days.
Jason Harries is targeting a first win on the World Series circuit this season with Wales. The series returns to action this weekend in Dubai where Harries is part of a team hoping to build from its efforts in round one in October.
Wales skipper Jevon Groves says his side have addressed a few points from Gold Coast and aim to 'hit the ground running' in the next two rounds of the World Series, kicking off with this weekend in Dubai before heading off to South Africa next week.
Wales Sevens manager Steff Thomas is hopeful his side can build from a quarter-final spot in the opening round of the World Series in Australia when his side take part in the forthcoming double header in Dubai and South Africa.