The phrase "a small bucket of" is correct and usable in written English.
It can be used when describing a quantity or container of something, typically in a casual or descriptive context.
Example: "She filled a small bucket of water to water the plants in the garden."
Alternatives: "a tiny container of" or "a little pail of".
She shouted something into his ear as she placed three glasses and a small bucket of ice on our table.
Composure regained, I delved into a small bucket of ingredients: prawns, fatty pork nuggets, vegetables, seaweed, tofu, all jostling for space in that soul-stirring broth.
So why do people practice like that?" Every teaching pro I talked to on the subject said recreational golfers should hit only a small bucket of balls, about 30 minutes' worth, at the range.
Those looking for more than a quick nip usually buy rum by the bottle (half-flask or full-bottle), a small bucket of ice and a soft drink or water as a mixer.
It was published by Random House in 1939, and Geisel clearly had some misgivings about it beforehand; nailed to the Godiva family tree, which he drew for the end papers, was a small bucket of sap labelled "Bennett Cerf".
Before the food appeared, a jug of water, basin and towel were passed round for hand washing, and then the bread was served, by men, with honey, a tub of margarine and a small bucket of mint tea.
Use a small bucket to remove any standing water from the tank of your grease trap.
Get two clean sponges, a small bucket full of warm water, some form of saddle soap and some neatsfoot oil or leather dressing.
Create a small bucket mix of a little salt and cold water.
Ortiz delivered their baseballs from a small bucket, flipping one to each of his former teammates as he worked the line, like a jolly Easter bunny giving out eggs.
In this week's issue of Nature, Seth Putterman, a physicist at the University of California, Los Angeles, and colleagues describe the fusion device, which is about the size of a small bucket.
