What is the ruling on buying dollars from a local bank with the local currency to transfer them abroad, given the significant difference between the bank's exchange rate and that of the black market?

If the transaction with the bank involves giving a sum in local currency in exchange for dollars, and the amount is placed in your account and you can withdraw it whenever you wish, then there is no harm in that. This is considered constructive possession. Dealing with a usurious bank is permissible out of necessity if the transaction itself is legitimate, such as in the absence of Islamic banks.