I bought myself a new bible: a translation known as the Jerusalem Bible. Like many of the bibles I own, it's a catholic translation, mainly because I want a copy that contains the deuterocanonicals (or what the protestants refer to as the apocrypha). If I could have found an Eastern Orthodox translation, then it would be much better because there are additional books in the Orthodox canon not found in the Catholic or Protestant sets.
I've read the various scriptures on and off through the years, but have not read through the whole Catholic canon because I did not have the heart to go through the law and the prophets. Once I gained the courage to reject religious belief, the impetus to read the scriptures disappeared. Still, it amused me to collect various translations and see how they differed from each other. For example, I've seen translations by Jehovah's witnesses, and noticed for example that their translation of the Gospel according to John 1:1-2 is quite different from the protestant and catholic translations. Unfortunately, I do not know any Greek, the only way I can see how theological bias can alter translations is by reading different translations.
Many people who claim they believe in the Bible but do not realize that what we consider to be "the Bible" is something that's not universally agreed upon. For example, the Catholic Church disagrees with the Protestant churches on the list of canonical books-- the Catholic Church has more books than the protestant list, probably because Martin Luther rejected the extra books as apocryphal; in turn, the Orthodox list (based on the Septuagint) has more books than the Catholic list. See the table in Wikipedia for a comparison.
One of the many reasons I have for agnosticism is this ambiguity in what is claimed to be divinely inspired; there seems no reason, beyond quoting authorities, for believing in any scripture. I'm much more likely to believe in the human capacity for self-deception than in the likelihood of divine intervention.
Having said that, I plan to do a more thorough reading of the Bible. I want to understand what other people believe, and to be better able to defend myself when people ask me why I do not believe in scripture. Aside from self-defense, I also would like to become more familiar with scripture because of how deeply biblical references permeate popular culture. So many literary works become unintelligible if one does not have some knowledge of the Bible. ( I suspect that, to be intelligible, a reader of Muslim literary works probably needs to read the Qu'ran as well; reading it, however, is surely a project for another day.)
I have read the gospels (more than once), Genesis, Exodus, Samuel, Daniel, The Song of Songs, Revelation, and skimmed some passages from other books, but I've never done a systematic reading. I may as well start now.