In the PPH it claims unconsciousness by nitrogen exit bag to be rapid - happening within a couple deep breaths. Why is this so?
I think, that information is inaccurate. A semi-conscious person may seem unconscious for naive observers who have never experienced the effects from inhaling gases like nitrogen on themselves. Formally, you probably can lose consciousness after 1 - 2 deep inspirations of nitrogen without doing the 3rd one, but you'd likely had to hold your breath for 10 - 40 seconds after completion of the last inspiration before complete loss of consciousness actually occurred. Note also that the PPH is written for old people (like 50+) who can be significantly weaker in average than 20 - 40 year-old adults, so fainting can happen faster for the intended readers of that book. When I fully inhaled nitrous oxide (which is a bit stronger sedative gas than nitrogen) in a single deep breath, losing consciousness completely took approximately 35 seconds.
I can hold my breath for 5 minutes while diving and be fine but inert gas inhalation will knock me out immediately? What are the biological/chemical processes going on to make this so?
When partial pressure of oxygen in the lungs is too low, they can do the inverse thing to their original purpose, that is taking oxygen from the blood and turning it into the gas filling the volume of the lungs, similarly to what commonly happens with carbon dioxide. Then you can exhale this oxygen.
Interestingly, you can also saturate your blood with CO2 if you breathe carbon dioxide at high concentrations like 30%. And even if you mix 30% CO2 with 70% O2, this won't prevent you from losing consciousness due to the excess of CO2 in the blood after breathing such a mixture for about half a minute.