Please ignore this useless advice. Leave the damn biner. Stick clip your way up or use it to retrieve a draw. Rap down from the top to get your gear. Climb another route and get to your draw(s).
You don't need to aid-downclimb to avoid leaving bail biners, you just need to be willing to take falls.
If you were able to hold onto the climb to hang the draw, then you should also be able to hold onto the climb to remove the draw.
briefly pull onto the climb, call for a bit of slack from the belayer, unclip the draw from the bolt, and then let go and take the fall.
Repeat at the next draw until all but the last draw remains. Lower to the ground off the last (lowest)draw. Then climb back up, pull the lowest draw off, and downclimb to terra-firma.
Alternately, go to the hardware store and buy some inexpensive quicklinks (i.e. screwlinks) - like a link of metal chain, but with a screw-gate. They can be purchased for far less than a biner, and one is easily kept on a harness gearloop. Check out the "rated working load" of the screwlink when buying - if it's at all more than your bodyweight, then it's more than strong enough for lowering off, because the desgned-in factor of safety on items like that are very high.
Probably better to ask this in the Sport-Climbing forum, as it sounds like you're talking about a sport-climbing scenario. Guess you could do the same thing for trad-climbing - but you'd have to trust all your pieces (you should anyway), and might lose some gear by falling on it and making it difficult to remove.