What's the best/most reliable credit card that does this?
I'd say either Wirex or Xapo.
Maybe Coinsbank, but I have never used them myself so I can't really comment on their quality of their product or anything like that. I've only touched Xapo which has worked for me every time if you are willing to provide some ID, and Wirex is one of the oldest anonymous CC providers around, you don't even need to submit your ID.
They were called e-coin before they rebranded.
If you want to pay your bills, look onto localbitcoins. In my country there are always offers to pay your bills for bitcoin on there, and for a pretty good price as well.
I would be careful with localbitcoins. A lot of people are getting in trouble with the law for running an "unlicensed money transfer service". Having someone pay your bills for you by using localbitcoins could be against the law in your state. All depends of course on the local laws.
Bitpay has a debit card you ca load and make payments with. It lets you hook it up to many accounts.
Monaco card i think is coming out with a 10% rewards card(current bid for one is 200,000USD).