So here's my head cannon explanation -- When Leia sensed the missiles inbound (clearly shown before they hit), she used the Force to wrap a bubble of air around her, cushioning the explosion and decompression. She was stunned, but not substantially injured by the blast because of it.
She regained orientation and Force Pulled to the ship -- too big to move the ship, so her body moved instead -- and she was able to get back to ship.
Equally not impossible to believe that if there WASN'T an airlock on the bridge, that there is a deflector screen on the bridge of a warship similar to that used in a fighter launch bay that can at least keep out a hard vacuum from the rest of the ship, to allow damage control crews access to the bridge while in space. Just because we didn't see it, doesn't mean it wasn't there. Sure, it requires some significant "handwavium" to be used, but ultimately, I'm fine with that.