Hi Jonathan,
Unfortunately Bluetooth isn't going to be an option. iOS is very particular with what devices or will pair with to send files and any Android device is listed as a no-go I'm afraid. Bluetooth sharing between iOS and iOS is fine as is Android and everything except iOS.
You have a few options. If you send him the original OnSong files (.onsong), my app will convert them for him. Alternatively you can export them as OpenSong XML files (which is what I think you are doing) - you might have more success if the XML file extensions are changed to .ost ) that way my app will know that they are OpenSong files. In OpenSong, the export set feature creates a set file which has links to the songs, but the song files are required separately, do they have to be included separately.
My recommendation firstly is to create an OnSong backup file containing all of your songs. Send your bass player (or wife's phone) a copy of this .backup file and he can import these in to OpenSong (which will extract the songs and convert them into OpenSong format). Then just send him a copy of the set list and he can make his own OpenSong set list (it literally takes about 1 min).
If you add new songs to your library, just send him the individual songs as above to add to his database.
If you could send me an OnSong set list, I could see if it was easy enough to cover to an OpenSong one.
Alternatively, most churches using OpenSongApp use a shared DropBox or Google Drive folder for the storage (you'll see how to do this on my website). That way any sets or songs created or edited are always kept up to date between multiple devices. If you wanted to do this on your wife's phone, you could make sure the songs were there and the set was created and saved, then all your bass player has to do is make sure his Kindle has synchronised afterwards and then he loads up the set you created which will automatically be available to him. This is how I keep all my devices in sync. It's also useful if the tech team are using the desktop version of OpenSong for projection as they also then have the correct songs and set.
Hope that helps?
Gareth