In Japan, people often bow (or rei in Japanese) to say hello, good bye and to show respect.  This in essence is why Japanese martial arts include bowing and since Jiu Jitsu is a Japanese martial art there is a good amount of bowing incuded.

It is worth noting that this is actually an efficient way of showing respect to groups and being polite and courteous whilst training.  Just imagine how much longer things would take if you had to shake hands with your training partner(s) everytime you started and finished training with them or how long it would take an instructor to shake hands with a hundred and fifty people at a regional course.  InJapanese culture it is also a good way to greet and say goodbye without actually having to make any physical contact ... but there's certainly a bit of that in Jitsu.

Beyond the politeness the rei is also used as an indicator to ensure that people know when someone is ready or has finished training.  It is an important aspect of health and safety in the dojo.  In what can be a very noisy environment bowing is a clear visual indicator (to those without significant visual impairment for whom additional safeguards are put in place) of acceptance and understanding.

On the basis that anything that everything worth learning in martial arts takes a little bit of practice, even bowing has a few aspects  and specifics to it that make it worth exploring in a little more detail.