I guess a legend like Bunyip that is spread across such a large area has many different forms
I think you don't have to have a big place to have different stories of something.
Since we got turned to christianity before we started to write down our legends, big parts of our old religion are lost. What we have from the time before the XI. century is mostly from scraps from the "reports" of people from other nations. We have a basic knowledge from the literature classes, and from then it's who read what theory. Oh, and we have folk tales I like to read from time to time, even as an adult - then again, most of the times you can notice a Christian touch on them.
My favourite creatures are the turul and the táltos horse.
The turul is a bird, possibly originating from the saker falcon, a kind of protector/guiding spirit (or, according to some, a god). It is said that, in a dream, it appeared to Emese, and showed her that a great river of kings will originate from her womb. Some time after she gave birth to a son: Álmos. (Some variants, but not all, claim that the bird itself was the father.)
After Álmos had grown up, he became a great leader, who united the Hungarian tribes - think of them as people resembling the Huns - by a blood oath, then led them to the West (Recipe for seven: pour wine into a cup, spice it with some blood from the tribe leaders. Get them to vow that Álmos and his descendants will be their leaders; also, they will try they very best not to kill each other while travelling, etc., then everyone can take a sip).
According to the legend, his reason to do this was that the turul forewarned him of danger by sending a dream: first eagles attacked him and his tribe, then vultures: the turul came both time and chased the other birds away.
(Note: It's a historical fact that Álmos was sacraficed before his son lead us into the Carpathian Valley. Grateful bunch, that we were.)
The Turul is also supposed to be one of the beasts that helps the táltos (Hungarian version of a shaman) to travel to the other world. The other animal is the táltos horse.
It plays a part in lots of folk tales, always as the helper of the main character. A typical storyline of our folk tales: there are three youn men. Their father (either a poor person or a king) tells them to go and try their luck (or they have to save one or three princesses). The bigger two fails (or just too lazy to even begin an adventure), while the younger one succeeds. If the main enemy is an "iron-nosed midwife" (basically an old witch) the girl can be her daughter with two foul tempered sister. In those occassions, the hero takes on a job (where three days count as three years - it's almost like waiting for an update here...), executing seemingly impossible tasks with the help of the girl. He either finds an ill, ugly, weak horse on the junk-heap, or the girl tells him to ask for it from the evil midwife as payment for his job. He has to feed the horse smouldering embers, rub it off, etc, before it turns into a magnificient horse, able to fly faster than the wind. The lovers (of course he would take the nice girl with him...) then flee on his back, while the midwife chases them. Mostly on a broom, but it seems oven-peel or sometimes a flat-iron also suffice as an aeroplane for the newly made mother-in law. The girl often throws three of her belongings to halt her (like a mirror that turns into a lake; a brush that turns into a forest, and so on), but it's the táltos that gets them out of there in one piece. (Or the one that brings the pieces of the hero to the girl before the happy end, so she can stick them together...)
If the main enemy dragons, there are usually three, stealing three princesses: the first having three heads, the second seven, and the thirds twelve. The hero goes there, battles with them (usually by knocking each other into the earth a few times, before the hero pushes the dragon so deep that only his heads are out, then kills it, after learning where it's riches are). He finds a táltos horse in each dragons stables, deals with it the same way as mentioned above, then brings them back with the princesses, so his brothers have wives, too. (I guess he is just clever enough to see the hardships of having three sisters as wives...
)
In some occassions, he tries to win the horse (and girl) from the dragon by fleeing on the horse. The dragon also have some own táltos, so it follows them and brings them back. As always, three time's the charm. (It can also kill the hero on brutal ways, leaving it to the horse to bring the body to the girl, who brings him back to life.) The horses often hate the dragon, so in one or two occassion, if I remember well, the hero actually persuades them to throw it off from their backs; the dragon falls to the earth and crushes itself. (Don't ask why can't it just fly like at the beginning of the story. Maybe the princess was a great cook and it got too fat...)
Oh, the horses also tend to have more legs then they should: six, or even eight, but not in every story.
They can also contain fairies, devils or kobolds, and more than one case, speaking animals (in threes).
Of course, that is just the "script" of the most frequent tales; there others with more originality. Seeing that horse sacrafice was a common occurence in the old days (especially if it's hair was white), it's easy to imagine that they could carry someone to the afterworld -
after they died, too. (Think of Saint Peter's horse.
)
(A tale of the latter kind, White-Mare's-Son can be found
here, if someone's interested. It looks like someone was on drugs when making this, but got some awards in it's time, and the maker knows his lore well. It's not the only variation, but the most known.)
(Now I don't have time to check it for grammatic errors, so please forgive me if it contains too much.
I'll check it again after arriving home.)