Ah, I see, The clue is that you're standing with a Bowline already tied around your waist!
Ensure your friend is well fastened to one end of the rope so they are free to hang (and are happy to fend off the walls with their hands).
Climb to the top of the pitch and then attach the rope to yourself as close to the bolt as possible and "jump" off the pitch. You're now "counterbalancing" your friend, so as long as their not more porkly than you, they should see the top of the pitch in no time.
If they're quite a bit lighter than you, then you could hard rig one knot into the bolt, attach a karabiner to the bolt and run the rope through the karabiner, leaving a bight. with the Bight you attach yourself in with a karabiner, and you'll be at a 2:1 disadvantage ie. every "one" you go down the casualty goes up "2", this effectively makes the casualty artificially "heavier" so you don't go flying down the pitch.
Or if the casualty is heavier, then you will need to switch the disadvantage. ie. Hard rig the rope for your casualty to the top bolt and send the bight down to the Casualties "D ring" or karabiner, then thread this through the top karabiner.
with the Bowline round your waist you can now "Jump" off and your heavier Casualty can go up "1" as you go down "2", clearly you will reach the bottom before your casualty reaches the top. so you might need to think of a way to "Lock them off" at the top before attaching a friend to the rope.