The visitors had taken the lead before Ahkeem Rose burst through the City defence to neatly finish past the keeper. But Bradford restored their lead when a great pass split the Town defence and was finished off nicely.
But the resilient Mariners weren't done and up popped Jack Keeble to head a deserved equaliser for Neil Woods' boys.
Speaking about the performance, the Town coach said: "We worked really hard. I'm really pleased with the way they went about it. To go a goal down twice, and there was a time when we wouldn't have come back, I'm really pleased with their mentality. I think it was a fair result in the end.
"To come back from that situation is development for us, it's progression," he added.
The Youth team are back in action on Tuesday afternoon at the Bradley Community Stadium when Scunthorpe United are the visitors. Kick-off is 2pm.
Watch the highlights of the Bradford game.