This is probably the best explanation, but the history is sketchy:
Old English bicce "female dog," probably from Old Norse bikkjuna
"female of the dog" (also of the fox, wolf, and occasionally other
beasts), which is of unknown origin. Grimm derives the Old Norse word
from Lapp pittja, but OED notes that "the converse is equally
possible." As a term of contempt applied to women, it dates from c.
1400; of a man, c. 1500, playfully, in the sense of "dog." Used among
male homosexuals from 1930s. In modern (1990s, originally
African-American vernacular) slang, its use with reference to a man is
sexually contemptuous, from the "woman" insult.
BITCH. A she dog, or doggess; the most offensive appellation that
can be given
to an English woman, even more provoking than that of
whore. ["Dictionary of the Vulgar Tongue," 1811]
Bitch goddess coined 1906 by William James; the original one was
"to complain," attested from at least 1930, perhaps from the sense in
bitchy, perhaps influenced by the verb meaning "to bungle, spoil,"
which is recorded from 1823. But bitched in this sense seems to echo
Middle English bicched "cursed, bad," a general term of opprobrium (as
in Chaucer's bicched bones "unlucky dice"), which despite the
hesitation of OED, seems to be a derivative of bitch (n.).