Bogosort vs bogobogosort
Not bogobogosort
The way you implemented your bogobogosort, it is actually faster than bogosort because of a few reasons:

After you successfully bogosort k elements, you immediately check whether k+1 elements are sorted.  This means that if on a previous shuffle, you happened to shuffle m elements all in order, then after you sort the first two elements you will immediately reach m.
For example, suppose you reach 5 cards and then fail.  You shuffle 5 cards and then start over at 2.  If those 5 cards happen to be in sorted order, you will immediately reach 6 as soon as you put the first 2 cards in order.

Because of point #1, your bogobogosort is actually faster than the bogosort because it only needs to sort n-1 cards instead of n.  After it sorts n-1 cards, it checks the order of n cards and may fail.  But in failing, it reshuffles n cards so that each time it sorts n-1 cards it has a 1/n chance of eventually succeeding.  So the total number of cards shuffled is on the order of (n-1) * (n-1)! * n which simplifies to (n-1) * n!, compared to the bogosort which shuffles n * n! cards.
I believe that the same principle applies at each step, so the time is even less than (n-1) * n!.  I'm not sure of the exact math but from running your program it appears that the bogobogosort runs in approximately the same time as the bogosort with one fewer cards.  I.e. Your_bogobogosort(n) = bogosort(n-1).


A proper bogobogosort
I rewrote your bogobogosort function to be like this:
unsigned long bogobogosort(int *data, size_t n) {
    unsigned long c = 0;
    size_t b = 2;

    while (1) {
        if (sorted(data, b)) {
            if (b == n)
                break;
            b++;
        } else {
            b = 2;
        }
        c += b;
        shuffle(data, b);
    }
    return c;
}

The key difference here is that after each success where it increments b, it reshuffles the deck to prevent point #1 above from happening..  With this change, I get output like this:
% ./a.out 6
    bogosort shuffled         1044 cards in 0.000013 seconds.
bogobogosort shuffled     54464568 cards in 0.500339 seconds.