Hi There,
I run my own business and I would use an account with my name on it. So you set up a new credit card account with your name on it. This represents money that the company owes to you.
When you pay the bills, you pay them using your credit card account in Quickbooks.
To claim the money for your credit card, you pay the money from the company bank account to you. and update the entry by passing an entry between the bank and your credit card account.
That should work and should be easy to manage what the company owes you when you use your credit card to buy company items.
Hope this helps.
RoscoPC