never mind I got it. Suppose |A|=|B|=m. Then we have a bijection iff we have injection. Since there are m! injections, we have m! bijections.
Or! You can note that a bijection and a permutation are in fact the same (for finite cases...the infinite case holds but with a slightly different meaning). Thus, how many ways are there to permute $\displaystyle m$ objects? [tex]m![/math\