There were definitely Christians in the Levant and in the Arabian Peninsula at the time of the rise of Islam; these would have been both Syriac Orthodox and Assyrian mostly. The Syriac Orthodox can be defined broadly as those Syriac-speaking christians who in the wake of the Chalcedon rejected its formulations and formed one of the various non-Chalcedonian churches. The Assyrian Christians were more or less those Syriac-speaking christians in the Sasanian Empire who were under the authority of the Patriarch of Ctesiphon. As for your question about bibles, we can reasonably surmise at least that the Peshitta-the Syriac translation of the Bible from the Hebrew and Greek-and perhaps the Diatessarion of Tatian were in circulation as well as a substantial corpus of oral literature and legends spread by Syriac Christians and Arab converts.