I have caught many away from the piling just drifting towards or away from the bridge. With that said, right by the piling, I have more success if I am anchored. Don't know why but my rationale is when anchored, I can get the eels right on the pilings, which is where I believe the fish go if up close. I also tend to set more lines when anchored that are deeper. When I drift, I tend to work the ledges and drops that are found as you move towards or away from the pilings and I don't generally set as deep (that could be the difference).
Check out the chumlord podcasts first and foremost (look up a post from lou and follow his link).
And yes, anchor or drift. Last time I was there was my first real striper trip and my first successful striper trip. We caught three fish in an hour on the anchor. Later when the tide switched we were drifting in and out of the pilings and a fourth came on an eel dropped in tight to the piles.