The island I spawned on had a 2 by 3 water pool. These blocks can be picked up by a bucket, but do not act as source blocks when placed down. So in this respect I only started with 6 buckets worth of water, not an infinite source like water normally would be.
Try to use a Glass bottle to pick it up, then place it in a barrel. It wont pick up the source...but you will get water from it
A bottle of water is the same size as a bucket. While you cannot set it down like you can with a bucket, you can fill a barrel with it, and then take the water from the barrel with the bucket.
