Perhaps you can use a flag in the fact table and the same flag in your calendar table. I guess that you are using two tables, bills table and calendar table and the relation is by the date field. If you can identify all possibles fiscal years and create a calendar for each fiscal year with a flag, and the bills table includes the flag too, then you can relation the tables by Date-Flag field.
Can you try it?
Tell me if you have any question.