Please try this:
tie a Standard Bowline (#1010) with a strangled double overhand knot (around the returning eye-leg, tail towards the tip of the eye (= around the ongoing eye-leg, tail towards the nub)) and then retuck the tail through the collar along the parallel pathway with the SPart…and try to “UnTIB” (untie without using the ends)
and as if by magic…
(Edit: BTW the TIB method to tie the knot is simple…)
But, if we tie an overhand (single, double…) around the returning eye-leg, with the tail towards the nub we can’t UnTIB! 
Xarax, IIRC, posites and shows that if we simply (immediately) retuck the tail through the collar along a pathway with the SPart of a standard Bowline (#1010 and #1034.5) we obtain a TIB Bowline (they are 4).
(http://igkt.net/sm/index.php?topic=4695.msg30330#msg30330)
Now we can extend the result by adding overhand (single, double…) knots as we’ve seen above.
Mark,
you could mention the method (as in ABok #1080) to discover/invent TIB Bowline suggested by Dan_Lehman,
(see http://igkt.net/sm/index.php?topic=4695.msg30331#msg30331)
–
ciao,
s.