From Longman Dictionary of Contemporary Englishfit/fill the billfit/fill the billSUITABLEto be exactly what you need This car fits the bill perfectly. It’s cheap and gets good mileage. → bill
Examples from the Corpus
fit/fill the bill• But it also fits the bill because people could order their favorite liquor.• It just happened that Bobby filled the bill in this case.• A floral design with a Regency stripe background, for example, fits the bill perfectly.• And the martini fits the bill?• Many other jobs get handed out simply because a minister happens to know some one who might fit the bill.• The martini perfectly fits the bill because of its simplicity.• The fact that she and Hugh happened to fit the bill seemed to give her every opportunity for finding out.• It is revealing, therefore, to see what sort of people are thought to fit the bill in these places. 