Some years ago I listened to an interview on CBC's "Quirks and Quarks" science show.
Some australian researchers actually conducted this experiment. (now this is all by fuzzy memory and I can't point you at a refrence).
They used a large, circular "tub" (tank actuallly) a couple of meters across.
They went to great lengths and days to allow it to stablize. Now the punch line -- lol --- I can't remember if they saw the effect or not.
However, what I do remember is that you will not see it in a bathtub. The residual 'swirl' is huge compared to the coreolis force and will overwhelm it. It takes extraordinary lengths and a symmetrical tank to give any chance at all of the effect appearing. However there is a force there and it can happen at some scale. You have to be very very careful in how the 'plug' is removed or this will introduce a swirl. This can not, apparently, be controled in a normal bathtub.