Good news, the Photobucket App on iOS has received an update!
Included in this update:
If you’re running out of storage, you no longer have to leave the app and purchase an upgrade on the website – you can do it quickly and easily straight from within the app, using the payment information already on file for the iTunes/App store!
You can access your upgrade options by first going to your settings:
Next, click on Get more storage:
Finally, select your preferred plan and follow the payment flow: