With your bank account number, thieves can commit ACH fraud to withdraw your money, create fraudulent checks, make unauthorized purchases, etc. Pretty easy to get routing number if you know the account number. I have had a bank account hacked, hence my caution. I don't mean to be snarky.
Anonymous participant Astounding. I get 5-10 scam calls a day, and 10-15 emails trying to scam. If I do a DTV I will create a new account specifically for this visa and then lock the account.