The Reds led 7-6 until Matty Blythe crossed twice just before half-time in a match which kicked off 15 minutes late when Bradford were delayed by a motorway accident. Play was then held up for almost 10 minutes in the second half when Chris Nero received treatment for a neck injury.
Nero was carried off on a stretcher with his neck in a brace and taken to hospital, but Noble said: "We are hopeful the injury isn't as bad as it first appeared. It was worrying for a time but it looks like Chris will be okay. There was no foul play involved and it was just an accident."
The Reds were thrashed 52-6 at Warrington in the cup last week, but Noble said: "This was a big improvement. We were unlucky to be losing at half-time and for 50 minutes I thought we were the better team.
"But then we contributed to our own downfall and didn't stick to the script. We didn't kick the ball as well as we had and didn't finish the sets as we should have done. But Andrew Dixon was the best player on the field and I remain positive about what we can do."
Jarrod Sammut set up three of the Bulls' five tries after switching to full-back for injured Brett Kearney.
Coach Francis Cummins said: "Jarrod is a player fans love to watch because they don't know what he's going to do. Danny Addy in the halves made us more direct and Luke Gale also pulled the strings. His team-mates joke he is the slowest half-back in the competition but he looked quick out there scoring his long-range try.
"I was pleased with Jacob Fairbank's debut. He is keen and wants to carry the ball. We stuck to what we tried to do and ground out victory.
"It was a nightmare journey here and at one stage we thought the game may not be on.
"We had little time to get ready and warm up but I have to be happy with that win."