How can I bundle my database file into my app, ready for a side load install?

You cannot package the database directly as read-write data (local state). If you only ever need to read from the database, you can just include it in your project and read it from Package.Current.InstalledLocation.

If you need to write to the database, but it contains some initial values you want to ship with your app, then you still need to include the database in your project, but then copy it from the InstalledLocation to ApplicationData.Current.LocalFolder if it doesn't exist when your app starts up.

You can all ways export your existing data base as SQL script and save it in your project assets. On the first run of your application you can create the Sqlite file in your LocalFolder, and run the script with CREATE and INSERT queries.