Bucket sort has uniformly distributed data Implementation of bucket sort is mainly useful when input is uniformly distributed over a range. So the ques here is what is the significance of having input data uniformly distributed for applying bucket sort? What happens if this does not hold?
Bucket sort will be slower if the data distribution is highly non-uniform.  The primary advantage of bucket sort over other sorting algorithm is that it is faster when the data is uniformly distributed; so if the data is highly non-uniformly  distributed, the advantages of bucket sort may evaporate.