Hey, Ron. I haven't paid enough attention to details while training to answer your question precisely, but fwiw...
I say it to whomever I'm training with as we begin; finishing, I say "Arigato Gozaimashita".
I've noticed a trend for saying "Onegai Shimasu" both before and after training. I have a couple of students from an Iwama dojo who do that and also say it to me after I've offered a suggestion on their technique. (I'd be interested in comments from people who do this.) I always say thank you in that situation myself.
In Japan, it's used whenever a request is being made and then having been made and granted, used again, i.e., they don't say thank you at that point as we do in English, they repeat "Onegai Shimasu" (in the logic of Jpn protocol, thanking someone at this point is presumptuous somehow).
...not directly pertinent to your question, but I hope it's interesting anyway. Take care.