Q. Does CMOS prefer “best seller” and “best-selling” per the dictionary spelling (over AP style of one word, no hyphen, for both)?
A. Because best seller (two words) is the first-listed spelling in Merriam-Webster (as of August 3, 2021),* Chicago would still recommend it, along with the hyphenated best-selling. But in 2017, when the seventeenth edition of CMOS was published, those—along with best-sellerdom and best-seller list (with hyphens)—were the only options listed in that dictionary. The spelling bestseller (one word) was introduced—as a second-listed equal variant—sometime after that.
As for AP’s preference for bestselling and bestseller, those are also relatively new, dating to May 2019. Meanwhile, the OED lists bestseller and most of its derivatives, including bestsellership and bestsellerism, as one word; the verb best-sell (with a hyphen) is the sole exception.
If this looks like a trend, it is—as a comparison of each iteration of “best seller” and “best-selling” in Google’s Ngram Viewer for books published since 1900 confirms (with a clear preference for bestseller and bestselling emerging in recent decades):
So unless you are obligated to choose the first-listed spellings in Merriam-Webster (e.g., for reasons of consistency in an ongoing project edited in Chicago style or to conform to house style), you’d be more than justified in preferring one word for bestseller and bestselling and the like. By the time the next edition of CMOS rolls around, we’d be surprised if these hadn’t become our first choices also.
[*Editor’s update: As of late 2022, Merriam-Webster has updated its entry and now lists one-word “bestseller” first, with two-word “best seller” as an equal variant.]