Well, if you're talking about simply making bill payments, start with your credit card. Your credit card allows you to make bill payments to pretty much everyone and anyone. However, if you're concerned about the security risks involved in online transactions, you can use online wallets like PayPal, Google Wallet etc.
Further, some banks allow you to make payments directly through online banking, such Bill Pay option with the US Bank. All you need is to input the bill payment schedule once in the system and make all the payment together. You can either schedule the payments or make them individually every month.