Can a collection company attach your bank account?

Yes, if they obtain a judgment on the past due claim and then file a Motion for Garnishment or Levy on your bank account. They however can not just take this action without the courts, and if they are claiming that they "will" attach your back account then they could be in violation of collections laws that aim to prevent making misleading or fraudulent claims to debtors.

If you suspect they are trying to mislead you into thinking if you do not pay them that they will take the balance from your bank account, or that they have the ability to do such actions without explaining the legal process, I would direct you to contact an FDCPA attorney as you may be entitled to damages for their violation of State and Federal collections laws.