link bill to credit card or journal entry

With this comment: "The expenses on the bill need to be categorized correctly."

Let's start Over.

The only reason the card account in QB is seen as increasing is because you entered the individual Purchases as "expense" from the Credit Card. If you did this, there are the details, already. The entry of the payment is against the Card account, because this is when you paid down that Debt Balance. The Check Expense lists only Credit Card Account as the category or detail type.

If you use a Bill to reflect the credit card balance, you are hiding CC debt in AP liability. If you never pay that bill or partially pay that bill, the reconciliation of the credit card account to its statement is impossible, because the Bill is treated as Paying the CC balance in full; you hid the rest in AP.

If you used a bill instead of entering the individual charges, then the Bill is where you broke out your spending details. However, you did not buy anything from VISA or AMEX; they are your Lender. They do not sell Office Supplies. You also did not buy everything on that one date. If you did this "batched bill" method and also paid it and all the purchases fall entirely in your fiscal year, then make sure this is now a Paid Bill and never do this part, again. And this method does not affect the Credit Card Account in the data file, so if you already put the details in as individual credit card charge expenses, this Batched Bill would have Duplicated these details and that is an error; the bill in this example is supposed to show only the CC account.

If you made a bill to pay the CC account after reconciling, and you didn't pay it, then it is safe to delete it. When you enter your real payment, simply do that correctly, as a check or paperless check Transfer, between Checking and CC. There is no AP involved.

If you made a Bill and also made the credit card charges, and also already Paid that bill, then you have an AP check and the bill needs to show only the CC account is being paid. Never have the spending details in two different entries.

If you entered a Batched bill, breaking out and categorizing the spending on that bill, and have not yet paid it, and did not put that in Credit Card Charge expense, then delete the bill and do the entries properly, for each purchased From name and each Purchased date. If you also already paid that batched bill, then do not also put the spending in your Credit Card account as expense entries.

The question here asked how to get a Bill to reduce the credit card account balance: if the bill is not paid, Delete it, since it isn't the right entry type. If it is Paid, then the check is linked to the bill and the Bill is supposed to show the CC account, which will reflect it reducing the CC account, even if the bill Never Gets Paid.

And this is why there is no Bill. That is your account activity statement.

Hope that helps.