There are banks that accept bearer shares companies. I can't really give you a list of banks, since in my experience bank tend to take a very case-by-case approach to this. That said, you can try in the Caribbean region, Mauritius, Seychelles, and throughout︀ Europe. Some banks will require that the shares are held with a custodian.
Banks will look for what is called the Ultimate Beneficial Owner (UBO). If Company A is︆ a bearer shares company that owns Company B and you try to open an account︇ for Company B, the bank will ask for details about Company A. You are going︈ to need a rather complex nature behind the company that opens the account if you︉ want the UBO to be unknown to the bank and be a bearer shares company.︊