The home side have enjoyed a barely believable league campaign so far this season and carried that form into the cup with a 17-3 victory.
The match started at a frenetic pace as both sides hit the ground running but neither side could find their way to the try line as both defended well or made errors when scoring opportunities arose.
Bedwas finally got on the board midway though the half courtesy of Lewis Robling's boot after the Drovers were caught offside. A second Robling penalty goal after 31 minutes put Bedwas further ahead before the Drovers' Cerith Rees replied to narrow the margin.
With three first half minutes remaining, Bedwas won a scrum and eventually moved the ball right through several pairs of hands to Budina who powered in from just outside the 22 for a try out wide. Robling's conversion went just wide.
The second half followed a similar pattern to the first with defences largely on top although Bedwas probably could have extended their lead but for passes to go astray or the wrong options taken. Similarly, Llandovery had chances to get back into the game but they couldn't add to their points tally as a stout Bedwas defence kept them out.
Bedwas ought to have added to the try tally but a couple of chances were wasted. However Robling added two more penalty goals after 45 and 72 minutes which combined with brave defence, saw the home side through to face Carmarthen Quins away in the next round.