Bowing when entering the tatami

Purpose of bowing

When Yoshigasaki Sensei simply left the mat at the end of the early morning practice (Kenkotaiso, Misogi, Meditation) during the 2010 summer seminar in Bosco Gurin, questions arose as to why he hadn't concluded the session with the usual group bow.
In the subsequent Aikido training session that morning, he explained the meaning and purpose of the bow.
In English, Yoshigasaki Sensei refers to it as "bowing," while in Italian he uses the term "saluto," meaning greeting.

Summary

The bow upon entering the tatami serves as a cut. It marks a cut between ‘outside the mat’ and ‘on the mat’. It is a change in mental attitude.
There are often people who practice on the mat even before the lesson begins. When they step onto the mat, they change their mental attitude with the bow and prepare themselves for the practise.
That is the complete (traditional) etiquette when stepping onto the mat.
When the teacher then begins the lesson, everyone bows together. And when the lesson is over, you bow again, returning to your everyday life.
However, some people also practise after the lesson. When they then leave the mat, they bow. That is the full etiquette.
However, etiquette can also change depending on the situation.
For example, if I have the same mental attitude outside the tatami as I do on the tatami, then this greeting is not necessary. That is why I do not bow when I step onto the tatami.
Even when I invite people to my dojo (Furusato) and they stay there for three days, this bow upon entering the mat is not required. For the entire three days constitute a single practice session. That is to say, in my dojo this bow, this greeting, does not normally take place.
So what is the purpose of the bow? This is why we do it.
So if you’re practising here early in the morning, and there are already people on the mats, this bow might not be necessary. But we can do a group bow to bring us closer together. Then, when we finish together, we bow together again.
However, if you are sitting in seiza at the end of the session (with everyone facing the wall and meditating on their own), it is better that you finish when you are ready. In that case, it is better not to bow together. Everyone finishes the practice at their own rhythm.
That is why I did not bow at the end this morning. Everyone should decide for themselves when to finish.