At the point in which we see old Biff give the Almanac to young Biff, there are only three DeLoreans, the highest number from the audience's point of view at a time during any period in the Trilogy: (1) DeLorean that Marty prime took to 1955 to escape the Libyans, (2) DeLorean that old Biff took to 1955 to give young Biff the Almanac, and (3) DeLorean that Doc and Marty seconde took to 1955 to retrieve the Almanac. The DeLorean in question or the "fourth" one (from 1885 in the mine) does not actually exist in this period and won't until Doc gets struck by lightning at 9:30 in the evening. When Doc is struck by lightning, the timeline instantaneously changes around Marty. In this new timeline, Western Union comes to deliver the letter at 9:31 to Marty, and the DeLorean is now inside the mine.
When old Biff was in 1955 to give the book to young Biff, that was in the timeline before Doc was in the past, so Doc was not in the early history books and the DeLorean certainly was not buried in the mine.
However, while it is entirely true that we do not ever witness a moment in the films where all four instances coexist, but the text "from the audience's point of view" above should hint at a solution. Once the DeLorean (DL) is sealed in the mine in 1885, consider what it would detect (if it were in a position to witness the comings and goings of its former selves): over 70 years of peace, then DL 1 arrives, then DL 2 and DL 3 arrive in some order; DL 2 then leaves at 6:38, DL 3 leaves around 10 PM, and DL 1 leaves at 10:04. DL 4 itself leaves soon after that. If we grant that all three of those instances DLs 1 through 3 continue to exist in the "final" timeline, then there should be no problem accepting this theory. Still not convinced? Consider the 100-year gap near the end of BTTF III when Marty takes the DeLorean on its final journey. 70 years into it, for a few hours, there are 4 instances of the car.
This question is actually one of the fundamental logical problems associated with the possible reality of time travel. These logical problems have actually lead to a number of prominent physicists publicly stating that time travel (meaning travel into the past) is an impossibility purely because there is no logical way to reconcile the varying paradoxes it would cause. In this instance, as stated in the prior paragraph, we the viewer are seeing events presumably as they happen for the first time. In this instance the fourth DeLorean would not exist until the DeLorean taken back from 2015 by the Doc and Marty has been struck by the lightning outside the tunnel. Once that has occurred the DeLorean will have been left left in the cave by Doc Brown in 1885 which means that the DeLorean will have already existed in the cave prior to Marty having gone back to 1955 the first time as it was left there 70 years earlier. The characters simply were not aware of its existence there until Marty is made aware by the Western Union telegram from Doc.
In other words, we experience time linearly from the perspective of Marty McFly. Most theories of time itself are not so linearly limited with all things always happening at all times. For the DeLorean to ever have existed in the cave in 1955 it would always have to have existed in that cave since being left there in 1885 and will always have to have been left in the cave in 1885. Thus we have a logical paradox.