Swift only. No Objective-C files required.
Here is another solution which uses SQLite.swift instead of FMDB.
1.: Get a valid path to your database file
Don't save the database file in your Assets folder, but add it to your Copy Bundle Resources list in the Build Phases setting of your current target. If your file is called myDb.db you can then get a valid path like this:
let dbUrl = Bundle.main.url(forResource: "myDb", withExtension: "db")!
let dbPath = dbUrl.path
2.: Access your database (without copying it)
It is possible to access your database now without having to (manually?) copy it. Just use the SQLite.swift library:
db = try! Connection(dbPath)
Notes:
The only thing I haven't checked yet explicitly is writing to the database. At least a read-only access does work like a charm though.