Screwing the floorboards down would help but you need to take special care in a bathroom. If you're lucky, any pipework will have been laid centrally under boards which means that you can add more screws close to the edge of them. In reality, it has been know for some hamfisted berk not to have kept to this ideal and so you'll probably be wise to lift a few boards to check.
Depending on what floor covering you intent to lay, screwing a 3 or 4 mm sheet of ply down with short screws every 6 to 8 inches will provide a lovely surface to lay decent sheet vinyl.
Not sure how well tooled up you are, but a decent battery drill/screwdriver is a worthwhile investment (
Screwfix and even BQ do some good ones for under £100)