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.
The Webb Ellis Cup visited Lampeter on Monday to recognise the fact that the town is celebrating a major milestone as it is believed the first ever game of rugby played in Wales, was in fact played in Lampeter 150 years ago.
Cardiff Blues U18 Girls will go into Sunday's Gemau Cymru with an extra spring in their step after Welsh internationals Elinor Snowsill and Philippa Tuttiett offered some last minute tips at a training session earlier this week.
Rob Howley and Josh Lewsey addressed more than 250 community club coaches and referees at the first WRU National Community Conference on the weekend. The volunteers benefitted from coaching masterclasses and workshops in a bid to connect all levels of the rugby pathway in Wales.
UEFA has today confirmed the Football Association of Wales (FAW) has been successful in its bid for the Millennium Stadium to host the 2017 UEFA Champions League Final on Saturday 3rd June, 2017 (kick-off: 19.45hrs GMT).
The winners of a filmmaking competition organised by the education charity Into Film and the WRU enjoyed a behind the scenes tour of the Millennium Stadium - and a chance to be photographed with the WRU's fire-breathing, rugby loving mascot, Scorch The Dragon, and Welsh international, Jake Ball.