All that can presently (June 2019) be gleaned from sheet music covers and by internet searching is that Kenneth W. Bradshaw has 2 works published between 1911 and 1919.
Of ragtime interest is Dat Cacklin' Rag (1911) published by The H. Kirkus Dugdale Co., Washington, D.C., USA.
Surfers are welcome to contribute information about this composer.
This list is arranged in chronological order and contains 2 works by Kenneth W. Bradshaw.
It does not claim to be complete and represents only the number of items located.