The data volume of a BMW Remote Software Upgrade is up to 1.0 GB. The memory space of your smartphone is only needed until the data transfer into your vehicle and is automatically deleted from the smartphone after uploading to the vehicle.
If no Wi-Fi is available, the app uses mobile data for some features. In particular, when using the map on the "Destinations" tab, mobile data could be used to download additional map levels and information. However, if possible, the map is buffered in order to reduce the amount of mobile data consumed.