You misspelling ‘you’re’ (you are) as ‘your’ (belonging to you) meant that the post technically was referring to ‘my gay’: i.e.: the gay belonging to me.
Since I am bi, and gay and straight are both kind of like half-bi, knowing ‘my gay’ was a pun, or play on words, referring to the half of my sexuality (being attracted to the opposite gender) which you didn’t mention (you mentioned my gay, but not my straight) but continuing the theme of your grammatical error giving the sexualities in the possessive.
The meaning of the line “for only I know my bi” is threefold:
• Firstly, it’s pointing out that the post said gay when I am bi, which was only there as a link to the line above, which is explained in the second paragraph of this overextended essay.
• Secondly, it’s a reference that I’m not out to that many people.
• Thirdly, it rhymes.