Take the battery to Auto Zone, Advance Auto, or probably any other place that sells batteries and have them load test it. That will either eliminate or pinpoint the battery as the problem.
When you hook up the jumper cables, are you connecting them both to the battery on your bug, or do you hook your negitive jumper cable to frame somewhere? If you are grounding to the frame when you hook up your cables, the ground strap from the battery to the frame could have a bad connection.
When you had the battery showing a charge, did anything have power when you turned the switch to the ON position? Did it do anything at all when you turned it to start?