Bradford enjoyed the lion's share of the play and, with more decisive finishing, they would have ended their own disappointing season with a deserved win.
Visiting keeper Wes Fotheringham did well to save a shot from Bermudian international Nahki Wells in first-half stoppage time, after strike partner James Hanson had flicked the ball into his path, and Wells had two more chances in the second half - both provided by Hanson.
First, he saw his shot blocked in the 50th minute and then fired wide of the far post 10 minutes later.
However, Bradford's best chance fell to midfield player David Syers in the 67th minute. Winger Will Atkinson played him through on goal, but his shot lacked power and Fotheringham saved.
Swindon, who were second best for most of the match, finished strongly, but the nearest they came to scoring was when Bantams keeper Jon McLaughlin turned skipper Paul Caddis' 20-yard free-kick over the crossbar before striker Paul Benson fired into the side-netting.