Can you sue a bank for allowing a company to withdraw money from your account without your permission?

If the withdrawal was a reversal of wire transfer or direct deposit that had been made to you in error, while the bank should have provided notice, they did nothing improper in making the reversal. (Or any other similar situation where it was an error to have transfered the money to you and the bank was just rectifying an error.) Or if you had given the company the information and permission it needed to access your account (e.g. you signed up for insurance or a subscription paid by monthly transfers from your accountt), then even if this particular transfer was wrongful, the bank did nothing wrong--you had given the company power to access your account, and the bank is under no obligation to check each transaction.

However, other than those  situations, it would seem that the bank was in the wrong, though it's difficult to say with certainty with so little information.

If the company wrongfully took money from your account, you can and should take legal action against them. If the bank wrongfully facilitated or allowed the withdrawal, you could procede against them as well--you are not required to go after one or the other, but may go against both, if both were in the wrong.