Is straight guys wearing women's underwear against the bible?

In Judaism and Christianity, the global injunction against wearing women's clothing can be found in Deuteronomy 22:5 (and vice versa). Christian doctrine tends to generally draw a distinction between moral and technical laws, when viewing the myriad commandments given in the Jewish Torah (or Pentateuch -- the first five books of The Bible). The former are considered binding today on all humanity, the latter no longer apply (according to boilerplate Christian doctrine). Likely, the cross-dressing would fall under the former, so cross-dressing is out.

However, Judaism holds that the entire balance of Torah commandments are only binding upon Jews, and non-jews are released from the overwhelming majority of such commandments. According to Judaism, non Jews need only be concerned with a very short list of commandments, among which are the requirement to establish courts of justice, abstain from idolaltry, adultery, murder, eating from a living animal (as in an amputated limb). Seven altogether, these are known in Judaism as the Noachide commandments, as they were first instituted in the time of Noah (Noach). By these limited standards, it's not likely that Judaism would consider cross-dressing sinful for non-Jews (for what that's worth). But, since the question was about what the 'Bible' says, that's the answer.