The global network of 3rd-party printers that print and ship orders placed on the Redbubble marketplace only do so after an order is placed on the Redbubble website. For this reason, dropshipping is not an option.
You're more than welcome to place orders on the site yourself and have them shipped directly to your customers. You'll have to do that manually, however, by adding the product to your cart, proceeding to the checkout page, and entering your customer's shipping details.
Our Bulk Order program is perfect for those looking to place large orders through the Redbubble marketplace. To get in, you'll need to submit the bulk order request form, which will require a Redbubble username (sign up here!).