Hi @Boourns82 and welcome to the forums! Your question would be better addressed to Zwift since it is up to any third party app to develop the link to Fitbit. For more details, check out this Fitbit Help Page.
I found this link to Zwift’s customer support.
That is not true. Fitbit must first broadcast the HR on low power BLE in order for Zwift to integrate, however Fitbit has chosen to broadcast.
Sorry - should be chosen NOT to broadcast
Best Answer@Chrisvlewis - It has been my experience that in order to link my various apps with Fitbit, I’d had to start with those apps. Maybe Zwift is different? Have you checked their site? You have to somehow give permission for Fitbit to share your information with another app.