No, we haven't got a clue either.
But this is Ankh-Morpork, remember.
It doesn't matter that seven-and-one Virtues outnumber the Seven Deadly Sins by one. In Ankh-Morpork, which gang do you think is going to win?
Bissonomy, like her sister Tubso, is a Virtue honoured by so few people (and even that was so long ago that nobody knows what it is any more, nor how to be properly Bissonomic or Tubsonian) that there is now no-one in Ankh-Morpork, not even from the Guild of Historians who can explain what the virtue was. You may be sure none of the Deadly Sins has fallen out of memory in the same way...
However, according to Chaffinch's Ancient and Classical Mythology, there was a Goddess Bissonomy who had two children by the great god Blind Io, and who was later punished for the sin of throwing a mole at the shadow of the Goddess Resonata. The god Epidity took it on himself to administer this punishment, which turned Bissonomy into a shower of oysters. (Look, they're Gods. They don't have to provide reasons.)
So we can gather that if the oysters fell into a congenial quiet tidal estuary, Bissonomy may live on in mollusc form, living the simple bivalvian lifestyle.
The stated detail of two children only does not suggest Bissonomy was the mother of the Three Disgraces. Their despairing stepmother, possibly...
We can perhaps also surmise that being Bissonomous does not involve a prohibition on throwing small mammals, nor does it prohibit you having children outside wedlock, but might have a taboo on eating shellfish. Who knows? In Going Postal, Moist von Lipwig looked at the statue in the Library and from certain evidential detail, surmised it had to do with kettles and a bunch of root vegetables looking like parsnips.
In The Compleat Ankh-Morpork, there is an advertisement for the unique business of the haruspex Jeremy Extispicy, Clairvoyant And Sausage Maker, who claims to be able to predict the future from pig entrails. One mystical cut of the pig is called The Rings of Bissonomy. This adds a Bissonomy association to either rings or pigs or possibly both. The Rings of Bissonomy run roughly along the line of the pig's backbone to just before the tail, where they meet the dispiriting Mount Of Unfathomable Harmonies. This may well be related to the quaint rural custom of hog-ringing, referred to in The Celebrated Discworld Almanak.
Annotation, or perhaps only a Footnote
Interestingly enough, in Judaism, a Roundworld religion where shellfish of any kind counts as traife (ie, the opposite of kosher), Rabbi Lionel Blue, religious thinker, broadcaster and the Jewish equivalent of Delia Smith, has a recipe for kosher shellfish. This involves using shaped and parboiled pieces of parsnip infused with fish stock prepared from aquatic life which the Almighty has declared to be fit to eat. Now Bissonomy was turned into a shower of oysters, so she would have an interest in not being eaten. And her statue depicts her with a boiling device and a bunch of parsnips....
Byssus, or Sea Silk, is a kind of fabric from the filament by which a kind of shellfish glue themselves to rocks and the sea bed
Bissonomy found in Turkey! Read []... a commentator on the article establishes an association with the Hindu demiurge Vishnumaya. Vishnumaya has both a male and a female form in Hinduism: the female form manifests as blue lightning, has the power of flight, and is a lesser sister of Krishna whose role is to protect and guard chastity. The male form of Vishnumaya is a son of Shiva who is a deity associated with war and combat; he also has attributes of disguise and concealment (a God of Camouflage). In pursuit of a mortal enemy who chose to hide in the waters rather than face him, Vishnumaya made the seas boil to drive him into the open. (A boiling device?)AgProv (talk) 21:10, 4 February 2014 (UTC)