I don't see a need for an additional conditional value list. The simplest way to see the budget number in a layout based on your Billing table is simply use the field tool while in layout mode to add the budget number field to your layout. This assumes you have the following relationship linking your two tables:
Accounts:: Department = Billing:: Department
Depending on what other relationships exist in your graph, you may have to create a new table occurrence with a different name to support this.