Click on the Submit button above the preview panel, and then choose e.g. "arXiv". There will be an option to download a .zip with the .bbl included. Once you click the button, it should show a "Please wait" message and take a while to build the zip. Then the button comes back, only this time it is a download link that will immediately download the zip archive.
You can also download the .bbl file separately. Clicking on the "Logs and output files" icon next to "Recompile", then scroll right down to the bottom. Then click on "Other logs & output files"; you can then download the .bbl file.