Are there any versions of the Jewish bible (Tanach) preserved today that pre-date Jesus (B.C.E.)? I feel that any version published after this time has a good chance of being biased towards or against Christianity.
Scrolls found in Ketef Hinnom contain the priestly blessing (of Numbers ch. 6) as preserved from the First Temple Era (700-650 BCE)
The Isaiah scroll found in Qumran: "has been carbon-14 dated at least four times, giving calibrated date ranges between 335-324 BC and 202-107 BC; there have also been numerous paleographic and scribal dating studies placing the scroll around 150-100 BC." These aren't an entire Bible, just the priestly blessing and Isaiah respectively.
The Nash Papyrus dated to 150-100 BC contains the Decalogue followed by the "Sh'ma Yisrael" prayer, with some variation from the Masoretic text.
Although not necessarily part of a cohesive unit, according to Wikipedia, fragments from Qumran (i.e. the Dead Sea Scrolls) identified thus far include every book of Tanakh except for the Book of Esther.
These mostly seem to pre-date even the earliest sects of Christianity (see cited Wikipedia page regarding the dating of the fragments).
The oldest manuscript of the entire Chumash (five books of Moses) to my knowledge is the Keter Damesek (Damascus Ms.) from the 9th or 10th century. (This should not be confused with another manuscript of the same name from the 13th century).
It should be noted that variation exists between the exact texts of the Dead Sea scrolls and of the Masoretic text. I believe that these consist primarily of differences in plene spelling. (someone please confirm). Although some, such as the Great Isaiah Scroll (1QIsa), show remarkable consistency with the Masoretic text, others, e.g. the Jeremiah scrolls, are quite different. From the introduction to Jeremiah in this English translation:
Two important scrolls are 4QJerb and 4QJerd, which reflect a Hebrew text that is very different than the Masoretic form of Jeremiah from which modern Bibles have been translated. [...] This is true not only in small details but also in major aspects. [...] 4QJerb and 4QJerd (before they were damaged) and the Septuagint present a version of Jeremiah that is about 13 percent shorter than the longer version found in modern Bibles!
Furthermore, (please confirm) there is variation in the texts of the Dead Sea Scrolls themselves.
Worthwhile to note, is that just as Christian scribes no doubt had biases and agendas, Essene scribes in Qumran (or whoever authored the Dead Sea scrolls) may have similarly had biases.
Also worth noting that traditional Jewish literature discusses when we correct the Masoretic text to fit with other texts, e.g. those of the Talmud. Thus, the Masoretic text doesn't hold the exclusive rights to the "Jewish text". For more on this topic see this article.