If I understand the question correctly, a payment to your credit card bounced? If that is the case you shouldn’t have much to worry about. Assuming you made the previous payment on time and have good payment history and most importantly made right on the owed payment, you should only be hit with a late fee.
If this is your first late fee, you should call your credit card company, explain the situation, and ask them to waive the late fee. This works for many people but just remember that your credit card company is under no obligation to do so. The better your payment history, the more forgiving they will be of the late fee.
When it comes to delinquencies that affect your credit score, most reported delinquencies are 30 days past due. This means that you have to miss one full payment cycle before your credit card issuer would report the delinquency to the credit bureaus.
If you have trouble with late fees, a simple trick is to use your bank’s bill payment system and always send in a payment that will cover the minimum fee. This can save you hundreds of dollars in late fees if have problems sending payments on time.