Bowing is very much part of Japanese cultural etiquette, and there is a lot that could be written about etiquette but I will leave it to you to search on the Ogasawara school of etiquette.
The very quick topic I wanted to cover in this blog is bowing during your pairwork practice, with a partner or a stream of partners.
There will be times when you practice sparring/free-fighting and frequently change partners you will bow when you first pair up and bow again when you have finished.
The beginning bow and the ending bow acts as a wrapper to all the practice that occurs in between. So, if you are doing all the 10 Kihon Kumite in sequence with your partner, various pairworks from your syllabus, or routines being passed on by the instructor, there is no need to bow in between each unit. There’s no need to bow when the instructor gathers you around for deeper explanation.
I’ve seen too many YouTube videos where people are slapping their legs and bowing all too often. Kihon Kumite number 1, number 2, number 3 and so on does not contain the bowing.
When you face your new partner and bow in the first instance, some schools will verbally articulate the phrase “onegaishimasu” similar to when we bow in as a whole class at the start of a session. You can Google the wider meanings of that phrase, but for us it is akin to “Let’s all work hard and do our best”. The end bow is the equivalent of “domo arigato gozaimashita”, thank you very much for that.
That embodies the mutual respect and spirit of training together.