On the first step of the Billing Run wizard, in instances where a customer has pending charges across multiple months or billing periods, select Bill pending charges issued on a specific date from the What to bill dropdown and the Date Range option will appear. Use this to ensure that only a specific set of service charges are billed.
Any pending charges outside of a chosen Date Range will be excluded as part of the current billing run. You can see which charges will be included in Step 2 of the Billing Run wizard, under "Preview charges".