On Ancestry, tick the Match all terms exactly box at the top; enter Frederick William Evans and Bedfordshire. I get 1248 hits. In the Military category there are 2 hits. One of them is your Frederick William Evans. There are 19 pages of his military records, most of them are duplicated, all are damaged. One of them is a note querying his date of death. Unit records show it as 14 Feb 1902, War Office records show 15 Feb 1902. The unit confirmed it as 14 Feb. He died at Lydenburg of peritonitis.
His medical examination on 13 Mar 1896 gave his age as 18 yrs 2 mths