Beth Slips Silently into the Room

Very nice, measured build up

Your story builds slowly, and that's good. It is a fairly short story, so you have lots of opportunity to write new chapters.

Two problems. First, the transition from them exchanging names in the bookstore to his issuing commands to her in his study is confusing. Second, there is no rationale for his wanting to spank her.

You should probably re-write the story, taking time to address those two points. You could also tell us about the way in which she became his sub.

There's lots of room for expansion and improvement, even though this is essentially a good piece of work.