I did those experiments with breath holds about 25 years ago, so my memories may be imprecise. As far as I remember, the peak of the urge to breath was felt somewhere between 100 and 180 seconds after the last breath, then it started to fade out. At 210 - 220 seconds it was weak already. I also remember that I pronounced the number of passed seconds in my mind, so my attention was probably distracted from the suffocation in some degree. Additionally, I artificially induced some anger in order to increase my willingness to resist against the desire to breathe.
That's indeed a very interesting question. But since trial experiments with a bag are too dangerous, I wouldn't ever do them. When I decide that I don't want to be living anymore, my first attempt will be non-trial, that is, with the intent to actually end the life, not just reveal some information.