Cross-Dressing Ruth and Naomi

Hirhurim has a post about cross-dressing, and the situations in which is permitted or not. Since I'm focused now on megillat Rut, I would point out a midrash that Ruth and Naomi dressed as men on their way back to Bet Lechem Yehuda, for safety's sake, such that they would not be harassed. (After all, they were two women traveling alone.)

The basis of this is Ruth 1:19,

יט וַתֵּלַכְנָה שְׁתֵּיהֶם, עַד-בּוֹאָנָה בֵּית לָחֶם; וַיְהִי, כְּבוֹאָנָה בֵּית לֶחֶם, וַתֵּהֹם כָּל-הָעִיר עֲלֵיהֶן, וַתֹּאמַרְנָה הֲזֹאת נָעֳמִי.

19 So they two went until they came to Beth-lehem. And it came to pass, when they were come to Beth-lehem, that all the city was astir concerning them, and the women said: 'Is this Naomi?'

if I recall correctly and deduce correctly, from the word שְׁתֵּיהֶם rather than שתיהן. And this was only until they came to Bet Lechem, עַד-בּוֹאָנָה בֵּית לָחֶם.