Most cases of fatal asphyxiation have occurred while using some form of mechanical means to achieve the affect. "Mechanical" means anything besides the hands, including bandannas and scarfs. It actually takes quite a bit of force to strangle someone with your bare hands, but it is possible if the person is pinned where the "strangler" can bring body weight into play. Whether a girl could do it to a guy depends on the girl and the guy. It is very possible to fracture the hyoid bone in the larynx which results in the epiglottis slamming shut involuntarily and the airway closing off. This event is fatal unless treated immediately with a tracheotomy (throat tube).
I'm not sure if you're just excited about the bondage/restraint part of this, or if you're actually wanting to go to the point that your brain is deprived of oxygen. If the latter, then you need to know that there have been some fatalities associated with this activity. In some susceptible individuals, and we don't' know why this is, the breathing fails to restart on its own when the airway constriction is removed. Many people get erotic fascination from the oxygen deprivation, but everyone involved in this needs to know that there is risk involved. Other than this, I'm going to have to leave this one to people who have actually tried it. :)