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 SWALEC semi-final draws threw up some mouth-watering clashes in the Cup, Plate and Bowl as the 12 teams aim for the Millennium Stadium Finals Day. All the semi-finals are to be played on the weekend of April 12.
Welsh whistler Rhys Thomas continues to scale the heights of the game as he prepares to be an official in this weekend's Hong Kong Sevens tournament, undoubtedly the showpiece event on the World Series calendar.
Wales International Ian Evans and Wales and Lions legend Scott Quinnell swapped rugby balls for paint pots at Tonna during the RBS 6 Nations. They surprised club players with a special clubhouse makeover to launch NatWest RugbyForce 2014 - a programme developed in partnership with the WRU to make rugby clubs stronger businesses by improving and renovating their facilities with the support of volunteers and the local community.
Fresh from claiming the Bowl honours in Tokyo last Sunday, the Wales Sevens squad have settled into their routine as they prepare for this weekend's Hong Kong tournament where Iolo Evans is aiming high, as WRU TV's Graeme Gillespie discovers.
The Welsh Rugby Union has recently teamed up with Prostate Cymru to help the charity launch its latest campaign to raise awareness of the disease. Members of the Wales squad helped produce a short video and promotional material for the campaign titled 'The Best Defence - is to know the FACTS'.
Defending champions Coleg Sir Gar reached their second consecutive Millennium Stadium final as they defeated Coleg Gwent in the WRU Wednesday Under 18 play-off. Watch highlights of their narrow 10-8 win here.
Wales Sevens head coach Gareth Williams has freshened up his squad for the next two rounds of the World Series in Japan and Hong Kong where Tom Williams, Owen Jenkins and Ross Jones make the trip along with returning Alex Webber and Craig Price.