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.
After two years in the international wilderness, Adi Taviner is hoping to make up for lost time when she takes part in her second Women's Rugby World Cup which kicks off in Paris next Friday where Wales take on hosts, France.
The WRU's Women and Girls legacy events - #TRY OUR GAME have proved popular this week with current players and newcomers to the game learning new skills and picking up tips from national squad players.
We caught up with Shona and Ellie from the Wales women team ahead of the start of the Women's Rugby World Cup in Paris next month at a recent women's training session to encourage and promote more women and girls to try their hand at rugby. #tryourgame
The Women's Rugby World Cup warm-up clash between Wales and USA proved bittersweet for centre Elen Evans. Despite being one of the star performers on the day on her 50th Test appearance, USA edged home 10-7 at Cross Keys.
Wales completed their Junior World Championship campaign with a victory over Samoa. Team manager Mark Taylor and No 8 James Benjamin reflect on a tournament which saw Wales win three games and lose two.