A major disadvantage of the detached tub stopper is that they are easily lost. I have customers who can't track down their tub stopper for one reason or another.
In this situation I highly recommend replacing the existing tub shoe for one with a built in tub stopper.
A tub shoe converter kit is a good option for this quick do-it-yourself project. The kit comes with an adapter that gives you two size options that will fit most drains.
Keep in mind that a Dumbell wrench is needed for this project. This specialized wrench fits into the tub drain and is used to loosen and tighten the tub shoe in place.