Doesn’t the Bible include the Jewish Old Testament?
Yes but it is not the Jewish version (the official version) of the Jewish Scriptures. It is the incorrect translation of the Tanach and as such is not accepted by Jews.
Plus Jesus is mentioned in the Christian Bible (obviously)and Jews would be forbidden from taking any vow on a bible that includes Jesus and his name.
>> Doesn’t the Bible include the Jewish Old Testament?
The “Christian” Bible contains both Old and New.