The proper manner of service of the subpoena depends on your state’s rules of civil procedure, You will need to consult the PA rules of civil procedure (assuming the bank is located in PA) to determine what is required.
Typically, the rules provide that proper service on a corporation (which is how banks are almost always organized) is made by either serving the registered agent in the state or by serving an officer of the corporation, if one is located in the state. Serving the agent is usually easy, so that’s the way to go if your state’s rules provide for that. But you must make sure that you follow exactly what the rules provide to make the service good or you may not be able to get the records.
Note that the rules also generally require that the opposing party be notified of the subpoena and they would have the chance to object. The bank will also, of course, notify the account holder of the subpoena and they will have an opportunity to object as well.
Of course, you need to be involved as a party in a lawsuit that has already been filed to issue a subpoena, and, as noted earlier, the information sought must at least be potentially relevant to the claim at issue in the lawsuit. The law disfavors “fishing expeditions” or using a subpoena for an improper purpose. If you are a party to a lawsuit, you probably should have an attorney representing you, and he or she will know how to get these bank records if they are needed for your case.