The original sentence, "How did you pay the bill?", is in the active voice. It asks how the subject ("you") performed the action ("paid the bill"). To convert this to the passive voice, we need to make the object ("the bill") the subject of the sentence. The verb "pay" needs to be changed to its passive form, and the original subject becomes the object of the preposition "by".

Let's analyze the options:

• Option 1: "How is the bill paid by you?" – This uses the present simple passive, which doesn't match the tense of the original question.
• Option 2: "How the bill is to be paid by you?" – This uses the passive infinitive, indicating a future obligation or intention, which is not present in the original sentence.
• Option 3: "How the bill has been paid by you?" – This uses the present perfect passive, implying the action has been completed, but it is not clear when this took place.
• Option 4: "How was the bill paid by you?" – This uses the past simple passive, which correctly reflects the tense of the original question ("did you pay"). It directly converts the active voice to passive voice while maintaining the question's meaning.

Therefore, the best alternative that expresses the same sentence in the passive voice is "How was the bill paid by you?" because it maintains the original question's tense and effectively shifts the focus from the person who paid to the bill being paid.