I want to say that B does X while A does Y. I'll give a small example: "While I go buying it for us, please wait here."
Two constructions come to my mind when I try to convey that two things happen simultaneously. Either verbs in て form or ます-stem + ながら.
I don't know wether one of the two methods is more suitable to express what is said in the sentence in question. Usually I've only seen ながら being used when the verb refers to one and the same person. But only rarely do I see ながら being used in my textbook at all. Here's one sentence with ながら out of my textbook: 音楽を聴きながら食事します。
て-form occurs more frequently for such purposes, and it also often indicates that an event happens while an action is being performed, like here: ジョギングをして怪我をしてしまった。
However, I think that also in these cases, the verbal expressions which were linked this way always referred to the same subject.
In the sentence in question, the subject changes. Therefore I fear that simply saying: "私は買って来てくれて、ここで待ってください。" could be ambiguous/prone to elicit misunderstanding. I thought about using は as a contrastive marker here, but I don't know wether that's legit here or not: 私は買って来てくれて、あなたはここで待ってください。
This becomes even more necessary if I drop the imperative. At least in my opinion: "While I go buy it for us, it is okay to just wait here." 私は買って来てくれて、(あなたは?)ここで待たなくてもいい。