It's easy to change which credit card you're using on Booth.Events.
First, start on the Billing page, hit "Change Card":
Billing Page showing "Change Card"
You can't change your card while in the trial period of a subscription. If you need to do this, cancel your trial and start a new subscription. Note that you're only allowed one trial, so you probably want to wait until close to when your trial expires before you cancel.
Next you'll see our payment processor Stripe's credit card change page. Fill out your new card details and hit "Save Card":
Stripe's change credit card page
After you save the card you'll be redirected back to Booth.Events where you can see the new card has been saved:
Billing page showing the credit card was changed successfully
All future payments will now be made on this card (-4444 in the example above).