Elk P. answered 05/05/19
Philosophy Literature Art Writing
There's a couple of things going on here: first of all, in Shakespearean times all of the actors were men anyways (because of sexism at the time in theater). So to have Bartholomew dress up as a woman adds to the hilarity of cross-dressing that was necessary at the time. On top of that, Shakespeare himself was fond of spicing up his plays with gender-bending antics because it was a little risque as well as titillating for audiences. Technically, Bartholomew didn't "have" to dress up, but it does add to the hijinks factor because disguise is funny by itself, but cross-dressing disguises are even funnier.
(Context: I am transgender and I love Shakespeare; I'm not saying "cross-dressing" is funny innately, but it was used for comedic purposes in Shakespearean times and even today in modern media. I love the gender-bending in Shakespeare because it reminds the audience that things such as gender roles, class, and piety are all sort of a farce to begin with, which is why his comedies are still lauded today.)