An excerpt from a well respected etymological source (Take Our Word For It) has this to say:
"...(broad) Evidently, it is not from being broad in the hips as is commonly believed. Broad originally meant a ticket (admission, transport, meal, etc.). The word was then applied to prostitutes (a pimp's meal ticket), then to women of loose morals, and eventually to women in general. It dates to 1911. Why a ticket was called a broad is uncertain. Playing cards were also called broads, so the similarity may be the answer. Or it could have something to do with traveling abroad.
Something for you to consider, anyway, and add to your data.
However, everyone seems to have a different explanation for broad's derivation. Others suggest that it comes from broadwife "female slave separated from her husband" (now obsolete) which was formed from abroad + wife. We could not find broad used to mean "ticket" in any of our sources.
As far as we know, broad to mean "woman" first shows up in a Dictionary of Thieves' cant in 1914. We'd be interested to see where the 1911 date (cited above) comes from..."