http://tdmskp.com.au/guide/index.php?title=Serendipity_Canyon explains how to drive there (with a google map link to show you).
To get there without a car, the only practical option would be to catch a train to Bell, then walk to Mount Wilson. I don't know of any tracks which might connect the two, so you would probably have to walk along the road. I have no idea how long it would take, but you would have to camp at least one night, because you couldn't walk from Bell to Mount Wilson, then do Serendipity, and then walk back to Bell in one day.
Of course, you could try hitch hiking.
Best option would be to find someone else who wants to do it who has a car. Either join a club, or maybe find someone here who wants to do it.