Hello, im looking to create a simple field on a saved search that will give me just the day of the month the customer is billed. (ex. Billing date 6th)

You should create an entity field on the customer record and then expose this field on your search, assuming the billing day is only one value.

If it helps and you already have the date field on your search, you can use a Formula (numeric) with formula TO_CHAR({yourdatefield},'DD') will return you the day of month.