Cut holes in the bucket bottom. Tie a rope through the top and cut holes about 50mm from the top around the sides. Tie a rope through the bucket and drop the entire thing over the edge so fresh water can flow through it. The ink will disperse at the same time. Have a second larger bucket ready with fresh water to place it in while you transport to a new spot. You can get 10ltr and 20ltr buckets with lids from Payless Plastics for a very reasonable price.
On a side note, squid can be caught all over the place. Just buy some luminous squid lures. Charge them under a head torch and cast on light line. They even put up a bit of a scrap.
For you Welly guys, the wall at Oriental Bay will produce squid in summer on a high tide under the lights. Just be careful lifting them over the wall. To the entertainment of another forum member I have been squirted in the face by an inking squid before at that location.