Here's an idea that will save you time and only requires a bucket and dustpan. Make sure the dustpan is clean and simply place it under the faucet with the handle extending over the edge of the sink. The dustpan handle will channel the water and act as a funnel allowing you to fill the bucket.
If the water splashes out of the bucket because the drop from the dustpan is too high, use a chair to raise the height of the bucket. ONE WORD OF CAUTION. Once you start filling the bucket, don't get distracted and walk away with the water running! I hope this idea works for you next time you are in a "big bucket, small sink" pinch.