The Talmud is very complicated, not every statement is a law, sometimes it is a commentary or the opinion of a certain Rabbi, sometimes a stipulation or refutation, however the quotes below should give you a good idea about Talmudic reasoning on certain issues.
The Talmud makes many suggestions that certain forms of bestiality may be legal under Jewish law.
ACCORDING TO TALMUD, ADAM HAD SEX WITH EVERY ANIMAL IN EDEN BUT WAS NOT SATISFIED UNTIL HE SLEPT WITH EVE
R. Eleazar further stated: What is meant by the Scriptural text, This is now bone of my bones, and flesh of my flesh? This teaches that Adam had intercourse with every beast and animal but found no satisfaction until he cohabited with Eve. (Babylonian Talmud, Yebamoth 63a)
SINCE TORAH LEGALLY STATES MEN MUST NOT HAVE SEX WITH HARLOTS “OR” DOGS, IT MAY BE LEGAL FOR JEWS TO HAVE SEX WITH HARLOTS “AND” DOGS AT THE SAME TIME OR PAY HARLOTS TO HAVE SEX WITH DOGS
Raba of Parazika asked R. Ashi, Whence is the statement which the Rabbis made that there is no adultery in connection with an animal? — Because it is written: Thou shalt not bring the hire of a harlot or the wages of a dog etc.;  and it has been taught: The hire of a dog and the wages of a harlot  are permissible, as it is said: Even both these — the two [specified in the text are abominations] but not four. (Babylonian Talmud, Sotah 26b)
FOOTNOTE 16: Deut. XXIII, 19.
FOOTNOTE 17: Money given by a man to a harlot to associate with his dog. Such an association is not legal adultery.
FOOTNOTE 18: If a man had a female slave who was a harlot and he exchanged her for an animal, it could be offered.
FOOTNOTE 20: Viz., the other two mentioned by the Rabbis.
YET AGAIN, SEX WITH HARLOTS “AND” DOGS MAY BE PERMITTED SINCE THE PROHIBITION IS AGAINST HARLOTS “OR” DOGS
Raba of Parzakaia said to R. Ashi: Whence is derived the following statement which the Rabbis made: Harlotry is not applicable to bestial intercourse? — It is written, Thou shalt not bring the hire of a harlot, or the price of a dog, and yet we learned that the hire of a dog and the price of a harlot are permitted because it is said, Even both these, two only but not four. (Babylonian Talmud, Yebamoth 59B)
FOOTNOTE 29: The beast which a harlot receives for her intercourse with a dog.
FOOTNOTE 30: A beast received as the price of a harlot who has been sold.