If you are the primary subscription holder for your Bitbucket account, you can update the existing credit card information by logging into your My Atlassian Account (https://my.atlassian.com, Atlassian ID = The email address you signed up with) and following these steps:
Log into My Atlassian. Your Bitbucket subscription will be listed in the "Licenses" section.
If the Bitbucket license details pane is not already expanded, click the "+" to view the full account details.
In the Credit Card section, select "edit credit card" to the right of the current card details. Enter the new credit card details and select "Save".
Once the credit card is updated, the new card will automatically be charged for any backdated payments and future monthly renewals.