Compacted volume = bank volume × (1 − shrink factor / 100). Typical shrink factors run 5-15% for engineered structural fill at 95-100% Proctor density. 100 BCY of fill yields about 85-95 CCY of compacted fill.
Structural fill placement is usually bid per CCY because that's what shows up on the finished site after compaction. Import fill, however, is bid per BCY (delivered) since the supplier sells you the in-place equivalent volume.
On the same bid, you may need bank cubic yards for cut excavation, loose cubic yards for hauling, and compacted cubic yards for structural fill placement — all of the same soil at different points in the workflow.