Is bride is feminine gender of bachelor?

No, the noun 'bride' is a word for a woman about to be married or just married.

The noun for a man about to be married or just married is groom.

The noun 'bachelor' is a word for a man who is not and has never been married.

The noun for a woman who is not and has never been married is spinster.

The word bachelorette is a more recent addition to popular culture, because the word spinster has such negative connotations.