We do not know what the specific rituals were, but observers of what is apparently Dionysiac death preparation left behind "instructions" of their preparation in at least forty different graves scattered all over the Mediterranean, from Olbia on the Black Sea to Macedonia, the Aegean, Greece proper, and Italy. They usually take the form of very small inscribed gold tablets. Two identical examples were found at Pellina, in Thessaly, in 1985. Both golden, shaped to look like leaves of ivy. On each is the following:

Now you died and now you were born, thrice blessed one, on this day; Tell Persephone that the Bacchic one himself has released you. As a bull, you leapt into the milk; Suddenly you leapt into the milk; As a ram, you fell into the milk. You shall have wine as your blessed honor, and ritual celebrations await you under the earth, and all the other blessed ones as well.

Why it would be Dionysus who is connected with the world of the dead is not totally clear. He is a very enigmatic god: there are many Dionysiac sanctuaries, but few actual temples; the theater was his temple, and every Greek theater was dedicated to him. Though he always received a bull sacrifice at Athens, elsewhere he more commonly got a goat, a rather unusual animal for Greek ritual sacrifice. The god was "born" twice, from a mortal mother and then again from Zeus. He was divine and immortal, but there was a tomb for him at Delphi. In Archaic art he is usually shown to be an adult, bearded, but also equally likely to be young and beardless, with long flowing hair, "shaped like a girl" (*thelomorphos). He frequently seems to cross gender boundaries: he wears a party dress and a woman's headband (mitra) often, and in Aeschylos a character calls him a "girlie-boy" (gunnis - in a fragment of Edonians). In Oedipus Tyrannus he is "the one who wears the same get-up as the maenads" (209-212).

He is a god of madness, of altered states, and of the spaces between black and white. He is the catalyst of transitions (though he shares this role with many other powers, including especially Artemis). All of this sums up to make him, in some way, an appropriate or desirable guide to the afterlife for some Greeks. The tablets like the one above show up about 400-200 BCE and none later (that we've found), so this seems to have been a short-lived but wide-spread fad. Bacchic mystery cults experience a grass-roots revival in the Roman Imperial period, however.

Plato talks about the purifying effect of ritual madness (telestike mania):

Madness, springing up and making prophecies to those for whom it was necessary, secured release from the greatest diseases and sufferings at one time arising from ancient causes of wrath in some of the families, having recourse to prayers and worship of the gods, whence, encountering purifications and teletai, it made healthy the one who had it for the present and for the future, finding release from the present evils for the one who rightly rages and is possessed. (Phaedrus 244d)

It seems that the Bacchic rites prepared one for the judgement to come after death (cf Republic 614b ff).

I have to go right now but when I come back later I will add some sources for further reading.