Hello Austenb welcome to Rootschat.
I love how the power of the internet can bring these stories back after so long. I hope our posts added some info for you if you didn't know them already

I've been having a look as records available have grown since the post began in 2007.
There is a medal roll for Alfred E Bedingham for 1899-1902 South Africa. A couple of listings as a passenger first an arrival in May 1907 on-board Kinsfaun Castle arriving from Cape Town Mr A E Bedingham age 26 police.
Also a departure for A E Bedingham in 1907 . Kinsfaun Castle On 5 th October bound for The Cape.
Both of those dates would account for missing 1901/1911 census.
Did he stay after the Boer war?
If you would like anymore info on his half siblings let us know.
Tazzie