Is my money and my bank account safe?
They would need your card to verify a bank transfer using your account details anyway so I would think it's fine if you cancelled the card and get a new one. Ring and double check with your bank's advice line if unsure though. Better to ask them directly than here.
The trouble is depending on the scam you're likely now on what's called a Sucker List, where the details of people who are known to fall for stuff get sold at a higher rate and you can expect more attempts.