Yes, you can pay bills with afterpay, but it depends on what type of bill you're trying to pay and how you're trying to pay it. If the company accepts afterpay, you can pay using the said service.
You can pay your bills by downloading the afterpay app, which will grant you access to the afterpay card that will act just like your credit card and spend easily. Also, you can use the Google wallet and apple pay as a platform to use your afterpay card to pay your bills up to your spending limit.