I don't think that the draining of the battery is being caused by the airbag removal unless that jumper you installed is somehow using power, which I would doubt. Just remove the jumper you installed, remove the cover that surrounds the heat/air controls, remove the four hex bolts for the heat/air control panel, pull it out as far as you can (the cables will only allow it to come out so much), then squeeze your hand in there and disconnect the wiring connector at the blue box (airbag computer). This will stop the dinging sound and will make the "airbag" light stay on constant, instead of flashing. If you want the airbag light gone altogether, you'll have to remove the gauge pod and cluster and take out the bulb for the light from behind.
As for the draining battery, I'd start looking for other reasons.... I've never heard of an airbag removal causing that. Maybe the battery it'self is old? Did you install anything else rescently that may be draining it? Stereo, amp, gauge, etc? I've removed the airbags in both of my Mustangs like I described above and didn't have any problems.
Hope this helps some and good luck with it!