At the moment, it would appear that they're equipped to hold a maximum of 3 individual adult bulls managed only in protected contact. They have a total of four yards, three of which are equipped to handle bulls.
As for cows, in theory, their only limiting factor is barn space, and if I had to venture a guess, if really pushed, they could probably hold at least 20-22 animals in total, and quite possibly more. Their barn is actually one of the largest in North America (only a few of the "super giants" like Oregon and Omaha have larger indoor houses), and since all of the indoor housing is both off display, and the barn itself is largely out of view of the public, they can devote 100% of the space to the animals, as well as expand fairly quickly and cheaply if need be, since expansion is purely for functionality, not looks or visitor experience.
Honestly, given the location of their elephant area, if needed, they could very easily double their indoor space, and add a number of large outdoor pens as well. Really the only thing holding them back from expanding to as large and diverse a herd as they could ever want is their own preferences on how large they want the herd. Selling off 3 or 4 of their breeding cows to the states would likely pay for all the construction costs of expanding, and they can get bulls for the cost of transport from Europe. With four cows currently breeding, and other 7 females under the age of 10, with more babies on the way, even the loss of four females would put basically no dent in their breeding program, and if anything just let it expand due to the extra space created.
During the off season (from October to mid May), basically their entire female group is allowed to just roam around the forests in the back of the property, and only stalled up at night. During the on season, of course, things are a bit different, but still, the herd is managed very flexibly.