The Jamaica international's first goal of the season, in his 19th appearance, and second half strikes from Callum McGregor and Jack Grealish ended a run of three matches without a win for Shaun Derry's men.
The Magpies started the day five points from safety following two defeats and a draw from their previous three matches during the festive period.
But Campbell-Ryce lifted the Meadow Lane gloom in the 32nd minute, taking possession midway inside the Bradford half and beating three defenders before guiding home a precise low strike from the edge of the box.
The game was safe for the home side in the 88th minute when Campbell-Ryce and Grealish combined to release McGregor, who calmly slotted home his 12th goal of the season.
Grealish, on-loan from Aston Villa, then profited from Enoch Showunmi's persistence and slid home a third goal in injury-time as Bradford's winless run was extended to seven matches.