Re: To bow or not to bow
To me, the big picture is that the bow serves as a non-verbal polite way of beginning and ending training (either as a whole class or during class with a partner). That asking for training and saying thank you for training is part of the fundamental etiquette of most martial arts.
It could be a bow, or a handshake, or a hand over the heart, or a bump of boxing gloves, but it's there. Because aikido comes from Japan and many of the folks who study the art are interested in more about Japan than just aikido, we bow. There is no reason that a group, if it has some problem with bowing, couldn't adopt another form of the ritual. I think the hand over the heart they do in Mecca is really elegant - they have replaced the bow with something that has the same meaning and doesn't conflict with their other beliefs. I think that's great. We've had a few Muslims in our dojo and none of them have minded bowing. If somebody ever does, I'll suggest that to them.
Even MMA fighters do it - they bump fists before the fight and then hug (even if they've just beaten the tar out of each other) after. The feeling is a little different, but even in the ring that little bit of tradition persists.
My $0.02 anyway....