Additionally, it does not make sense to directly compare the process of compilation of the Bible and the Qur'an because the two scriptures are quite different structurally and in terms of the historical circumstances surrounding them.
The Qur'an is much newer than the Bible, much shorter than the Bible, emerged in one region and in a short span of time. There has never been any question of what portions of the Qur'an to consider canonical. It was also all in a single language and dialect. Stylistically, the Qur'an is internally consistent indicating it is the work of a single author and does not have interpolations (whether or not one considers that author to be God, it still has a single "voice"). While, at the time of the Prophet, Mecca and Medina did not have sophisticated means of producing books, it was not long before advances in those areas, such as the use of paper, came to the Islamic world; and, in fact, it was through the Islamic world that some of these technologies were transferred to Europe.
In contrast, the compilation of the Bible is much more complicated. The scriptures are much older, span a broader length of time, and there is a lot more complexity with respect to how it came to be a single text. (There are numerous works on this subject available.) It becomes even more complicated if one considers both the New and the Old Testaments. It is not as if someone 2000+ years ago held out a book (or, rather, a scroll) called "The Bible" that is exactly the same as you find today; there was a process.
So, from a purely historical perspective, there are very different circumstances surrounding the compilation of what today we know as the Bible and the Qur'an, and the nature of the two books is also quite different. Therefore, it is not a one-to-one comparison and it is best to look at the compilation of each scripture separately and consider the validity or authenticity of each one separately.