Hell, there's not even any evidence that Kit was actually homo- or bisexual, except for a single line in the Baines libel ("All they that love not tobacco and boys are fools") which was attributed to Kit by somebody who was trying to get him killed. And some vaguely slanted/slanderous comments made after his death about the circumstances thereof--which are the same sources that give us the inaccurate information that he was killed in a tavern brawl, so we take with a certain amount of salt.
Oh, yes, and Kit included two homosexual relationships in his plays--one in Edward II, and one in Dido.
So where did this scurrilousness come from?
Fiction writers and literary critics. We made it up. Based on some textual suggestiveness and the endless search to have something interesting to tell people about a writer about whom all the existing evidence could be typed on a 3x5 card.
Because it was interesting. We are naughty that way. Naughty, naughty, naughty. Which is why you should do your research from histories and primary sources, and not from fiction. *g*
There's also no historical evidence that William Shakespeare died of syphilis (or that he was bisexual). We made that up too. Based on a couple of references to venereal disease in the sonnets and the late plays. (The bisexuality thing comes from a whole buncha love poems to a young man of inadequately proven identity--and even existence.)
As a writer, I find this amusing, because by this theory I am certainly a torture, kidnapping and rape survivor, based on the content of a couple of my protagonist's histories. Also a military veteran. I'm also probably male and possibly immortal. *g* I might also be Richard Feynman.
Textual evidence ain't worth the paper it's printed on.
That said, I've read "Hero and Leander." And I think I know whose butt Kit was checking out. Besides, it's interesting, isn't it?