If you separate a bible, you have actually many books therein. Also, there are, as you pointed, many "bibles", that is, not only different translations, but bibles formed by different sets of books -- some books are accepted here, some are rejected there. If you take the tipitaka, it is also formed by many books. Correspondingly, there are different versions and editions of it.
So, christianity, just like buddhism, produced many "books" (Matthew, Mark, Acts, Romans, Revelation etc, on one hand and, say, Majjhima Nikaya, Dhammapada, Khandhavagga, etc on the other). Christianity, just like buddhism, had groups selecting and discarding texts through time, establishing a certain canon for them.
An early example of this the buddhism councils.
On the christian side, this reminds me of some books I've read from a catholic father about the First Council of Nicea and how (overly simplifying), part of it, was about determining a christian canon -- that is, selecting the books that were being used by churchs, that show some consistency among themselves, etc, and apparently burning ones that were not (something to do with new sects popping up with corrupted texts to take advantage of the trends). But wikipedia presents material that disagrees so, this may not correspond to fact. However different, processes of determining what books form a certain canon still took place through time.
This just illustrates the point that there is a historical process, whatever it is, in both traditions, involving people who compiled what is part of the canon (call it a bible, or a tipitaka) -- and, in face of apocryphal material, what is not. Also, some groups may decide to preserve early material, rise the criteria for acceptance, and see late material with different eyes, while other groups may decide that some late material stands in equal footing, or is a legitimate continuation of (and fundamental contribution to) the early ones.
For example, Paul of Tarsus came in after, but his writings were welcomed in the canon (I wonder if any early group rejected his work?). Similarly, Nagasena came many years after the Buddha's parinirvana. So did Huineng.
Finally, both traditions had many authors publishing books on top of the core texts.
So, it seems to me the difference is the physical limits that a physical book imposes on the number of pages. While the bible can be formatted as a single physical book, I think it would be a challenge to have a unitary physical Tripitaka.
But, again, this is the electronic age of Kindles and such...