Kopczak, 23, was stretchered off in the first half but X-rays have revealed no fracture to his leg.
The Bulls are awaiting the results of further tests to determine the extent of the injury.
Bradford won the game 18-16, with star signing Matt Orford making his eagerly-anticipated debut.
Hull KR took the lead through Paul Cooke, but Orford was instrumental in turning that deficit around, first setting up Michael Worrincy with a kick and then breaking the line in the move which resulted in Stuart Reardon‘s try.
Orford was again involved on 64 minutes when his short pass sent Elliott Whitehead in by the corner, and although Rovers had the final say through Kris Welham, Michael Dobson was unable to land the conversion to hand the win to the Bulls.