There are marial arts classes here in the North Texas area that do teach dealing with an armed attacker and don't require a long-term contract.
The point of a martial arts program is not simply the transfer of knowledge, but a disciplined application of that knowledge at the moment it is called for. Training to the point where "the training takes over" requires continued repetition over a long period of time. In order to get his black belt, my son had to demonstrate the ability to disarm an attacker armed with a knife. While he learned the basic technique on his first day, it took two years for him to get to the point where he could consistently take the knife away from someone larger than he was.
In Asia, where most of what we call "martial arts" originate, bowing is a sign of respect for a teacher or superior. As used in martial arts in the United States, it teaches situational awareness (i.e. be aware of who around you outranks you and is entitled to the respect of a bow), discipline and humility.