I doubt that this is possible unless STRAVE would implement this in their app. I cannot see any reason why they would do that. There is no widely used Bluetooth Mass Storage profile. So, any implementation would be non-standard and therefore would requires constant maintenance as APIs e.g., from the OS or some required stack change.
On their web page all they need is login and file upload (which is implemented inside all browsers) and GPX decode.
Look at how Garmin has implemented this. You use their app to download the activity from a watch over Bluetooth. They have a contract with STRAVA to upload new activities from Garmin to STRAVA automatically. Or you upload the FIT file using the STRAVA web interface.