In order to "offset" you have to have a debt that's owed by A to B, and a debt that's owed by B to A. One debt gets offset against the other.
In this case, you have a deposit debt that's owed by Bank to Signer. But the debt you want to offset is owned to Bank by LLC, not signer. Because the debts aren't between the same parties, there's no right of offset.
Now if Signer has guaranteed all of LLC's obligations (or at least overdrafts) to Bank, then you have mutual obligations to set off.
Nobody's perfect, not even a perfect stranger.