It is possible to export a TCX file for any Wattbike session stored on the Hub. TCX is a widely supported file type and can be used with services like TrainingPeaks, Strava, Golden Cheetah etc.
To get the file, log into your account at hub.wattbike.com and navigate to the particular session.
On the right hand side a little way down the page you'll see the share box (shown below), just click the button to download the file.
There is no method to bulk download Wattbike sessions at the moment.