From a cursory glance at the 'History' section it appears that the institution became the KBGS in about 1928.
I have just noticed that on a photograph of myself in my first year at KBGS circa 1956 the badge on the blazer has only the 3 letters KGS!
Why is this so???
The "photos" section carries a few from the early 1950s, in which the monogram KGS is clearly visible on blazer pockets. As the pictures are in monochrome, it's difficult to see if they were in House colours, or whether that system was used only briefly in the mid-to-late 50s.
During my first couple of terms in 1958, House colours (in my case the Longsden purple) were prominent on ties caps, badges and scarves. To the best of my recollection (by no means infallible!)the badge monogram didn't include letter B.