No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
For Bank of America, go to the Bill Pay tab and click on "Add a new pay-to account" Search for what you want. (I just searched for "Chase Credit" and it finds "Chase Credit Cards".) Select the one you want, and you will be asked to provide account number (If it cannot be found, you will also need to provide name and address of the company).
It's then set up as one of your payees, and any time you want to push, just select it, add an amount, and it will push the payment (and tell you when it is scheduled to arrive).
I don't have a Chase bank account, but all my bank accounts support something like this.