Is expiation obligatory upon one who swore by Allah to pay a bill, but was unable to pay it due to the unavailability of change, and so another person paid it?

If you firmly resolve in your heart that no one but you will pay the bill, then it is a binding oath (yamin mun'aqidah). You will be in violation of the oath (tahannuth) if you do not pay, and atonement (kaffarah) will be incumbent upon you at that time. However, if you did not firmly resolve this in your heart, and you spoke merely out of habit, then it is a vain oath (yamin laghw) and carries no consequence.