Given the etymology of this sense of the word 'benedict', I would not expect to find any true feminine forms (other than neologisms).
From the OED:
1.B.1 A newly married man; esp. an apparently confirmed bachelor who marries. [From the character of that name in Shakes. Much Ado
[1599 Shakes. Much Ado v. iv. 100 How dost thou Benedicke the
married man?] 1821 Scott in Lockhart (1839) VI. 313 Wish the
veteran joy of his entrance into the band of Benedicts. 1843
Life in West (L.) He is no longer a benedick, but a quiet married man.
Your initial choice is actually probably your best bet. 'Bride' can refer to a recently married woman and this sense has been in use since at least 1000 CE. From the OED for 'bride':
1.a A woman at her marriage; a woman just about to be married or very recently married.