It appears that the little mirrors are square. That means that the surface cannot be entirely covered because there must be nonsquare spaces between them in order for squares to cover a rounded surface and form a sphere. If the size of the mirrored tiles is a constant, the number is going to depend entirely on the size of the ball, whether small enough to be a Christmas ornament or large enough to make a ballroom sparkle.
There is evidently a standard size for the mirrored tiles because this one advertises smaller tiles as a selling point.
I’ve made a rough visual count of the top half of one quadrant on the 8” ball at the second link above. The bottom half of the quardant is going to match the top half, and the whole ball woud be four times a single quadrant. There are roughly 100 tiles in that 1/8 area I counted. So that means there are approximately 800 tiles on this small disco ball. If this does indeed feature smaller-than-standard tiles, the number on a regular ball would be lower. I’d say pick an illustration and count.