I like apple as well, but I haven't tried any bottle stoppers out of it (yet.)
As far as the gap, I had a pretty experienced turner suggest to me last year that you use a washer with an OD a bit smaller than the flange of the stopper, and basically turn a chamfer down to it. It leaves a gap, but it's uniform looking and eliminates the problem of having to square the bottom of the blank exactly to the axis of the hole you drill it.
I've tried that on a few, and it works/looks well.
Gary
Nice I like turning apple wood. If you don't mind a critique try making the bottom a bit concave so the edges are tight to the stopper. unless you meant it like that it just looks like it has a gap