So, going over of a read of the bill, specifically the definitions in the overview. The bill specifically bans "adult cabaret entertainment" which it defines as:
adult-oriented performances that are harmful to minors, as such term is defined under present law; feature go-go dancers, exotic dancers, strippers, male or female impersonators, or similar entertainers; and include a single performance or multiple performances by an entertainer.
And further defines "harmful to minors" as the present law under Tennessee law:
that quality of any description or representation, in whatever form, of nudity, sexual excitement, sexual conduct, excess violence, or sadomasochistic abuse when the matter or performance:
(1) Would be found by the average person applying contemporary community standards to appeal predominantly to the prurient, shameful, or morbid interests of minors;
(2) Is patently offensive to prevailing standards in the adult community as a whole with respect to what is suitable for minors; and
(3) Taken as a whole lacks serious literary, artistic, political, or scientific values for minors.
So, for example, a man, dressed as a woman, reading to children would likely not qualify but for the second caveat, which is the most difficult to uphold. After all, very few people would balk at the show in show "Ms. Doubtfire" seen at the ending of the film of the same name. Nor would anyone find a historically accurate production of Shakespear's work (i.e. all male cast) to follow under this (At least one play (Merchant of Venice) pokes fun at the fact that everyone knew it was all male cast, but relying on the character of Portia appearing in drag for an extended period of time (The gag being the actor playing Portia was essentially a man, pretending to be a woman, pretending to be a man). Nor a Bugs Bunny Cartoon (the distinction here is the audience is well aware Bugs is pretending to be a woman... Elmer Fudd is just too stupid to notice.). Hell, I would say that much of the work of Eddie Izzard (save for some choices of language) are fine enough to avoid this, as he insists, he is a transvestite and finds women's clothing more comfortable to wear... and it's not the point of the show beyond that.
Where it would probably catch is if the Drag Queen Story Hour is making the performance overly sexual in nature or drawing to much interest to sexualized elements of the drag apparel.
That said, what will determine if this is permissible is through the testing of court cases. That said, we regularly limit access to minors to performances that are "adult entertainment" already, and I've seen some drag shows that are clear their appeal is adult in nature, so it's not something that is historically out of left field.