I know that, I can use Wifi even, but I prefer BT. Also I would like to know why it does not works. The device is not cheap and should work as it should.
What happens when you try to update over BT? Normally the watch will pull the update to the watch with the help of Garmin Connect. Then it will notify you to install the update when you are not training. You can also manually select to install the downloaded update.
It takes longer time before you get the update over BT. Have you made sure Garmin Connect is running and is allowed to use background data? Never ever force close the Garmin Connect app.
You must allow the app to use background data and keep it always running since it takes long time to download the update. So, never force close the app. Keep it like that for a week and see if you get the update to the watch.