I always assumed that the girl in the song was Billy Joe's girlfriend, and together the had a baby, either a hidden pregnancy, a premature baby, or an aborted child. They threw the child off the Talahassee bridge, and Billy Joe couldn't live with himself afterwards, so he jumped of the bridge and committed suicide. That's my theory.
There is a site that has a bit of information, but the song always has been shrouded in mystery, and Bobby Gentry never revealed the the secret.
Here are a couple of links. The second one is a very interesting read:
http://www.progression.co.uk/reviews/profile.htm
http://www.geocities.com/odetobobbiegentry/ghannah.htm
Cathy
http://www.cathycowette.com