Hello Jamie,
The situation is the same here on Bibledit for macOS.
Any such Bibledit on macOS, or Windows, and so on, has a bit fewer possibilities than the Bibledit Cloud version.
One of the differences is what you are seeing.
If the same app, Bibledit for macOS, is connected to Bibledit Cloud, and the user's rols is high enough, the stylesheet can be edited and selected.
A work-around for you would be to temporarily connect your Bibledit software to the Bibledit Cloud demo, see menu Settings / Cloud.
But be aware that in such a situation your Bible will be uploaded to a public demo, and may be edited by the public too. It's good to have a backup of the USFM in case you go for this work-around. But at least, this gives you the option to select the stylesheet used for export or for editing.
I guess the current functionality may feel a bit limiting. One option would be to submit an issue on GitHub for a future improvement to the app.