I tried to google it, but failed.
I imagine there are details like which version of the bible that make this hard to answer. I won’t specify anything.
Well, entering number of bibles printed each year into Google gives you a No. 1 link here, extracting from which:
In celebration of the 550th anniversary of the printing of the 42-line Vulgate Bible by Johannes Gutenberg, the inventor of movable type. The November 18, 1950 edition of the Antiquarian Bookman Magazine reported that by the end of 1950 (the 500th anniversary of Gutenberg’s invention), over two billion Bibles and parts of bibles will have been printed, with 25 million more being added each year. At this rate, the total number of bibles printed by the year 2006 will exceed four billion copies, in thousands of languages and editions. This makes the Bible the first and undisputed best-seller of all time and no other book is likely to take its place.
Perhaps this offers a starting point. 
I’ve seen several times the claim that the total number of Bibles ever printed is more than six billion.