First off if the bank did screw up they need to be held accountable. But based on what you wrote here it appears as if you are truly at fault. If you caught your misake "immediatly" you or they should have been able to cancel it.
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http://www.bbt.com/bbt/business/products/onlinebanking/faq.html#324
Can I modify or delete a scheduled payment that has not yet been sent?
Yes. All payments can be either modified or deleted up to 7:00 p.m. Eastern Time on the processing date.
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If they didn't cancel it and you got an "overdraft fee" that would mean that they paid the $10,000. Since you had $38 left and appear to keep a low balance, I would guess that they did fix it and only paid the $109. As banks are not going to let people get $10,000 in the negative, even people who generally keep high balances.
But since you didn't appear to have $109 in your account, that put you into overdraft. That is NOT their fault. Now, that is just based on the little that is posted here. If you have more details that may clear some of it up.