Statements of what is owed. In this record the word carries weight — bills are the clock the escape runs against.
Anglo-Latin billa, a variant of Latin bulla (a seal, and by extension the sealed document it closed) — the same root behind 'bull' as in papal bull, and behind 'bubble'; a bill was first the document, and only later, by the 17th century, the amount it stated.
A statement of what is owed, and in the record this word belongs to, the clock a body is racing against — not abstract debt but a deadline with a number attached.