Similar to what SG said. We see in BoG that Goku can breathe fine just outside of Earth's atmosphere despite Vegeta dying from being left in space in the next arc. Bardock probably wasn't far enough from Planet Vegeta's atmosphere for it to have negative affects on his health.
At least in the manga we don't have confirmation if he went to space to confront Freeza. As for the special though, maybe yeah, he was still within the atmosphere as we don't know how far he was (Goku could battle Beerus in the stratosphere and exist there without tiring himself much) or he had good lungs and could hold his breath for a while