Before anything else I want to stress out that in my opinion if you don't speak language and have no intention to learn it to some extent, asking for a phrase just to address someone does not make much sense. As a monospeaker she still will answer in Russian and then what?
I'm not big fan of this borrowing, in fact I actually dislike it however the sad truth is that de-facto can be treated as borrowing, it's quite exotic but still you can see "воркаут" in the wild. Here are quotes from Russian newspapers:
- Инвалид из Узловой мечтает о тренажерах для воркаута (link).
- Здесь заменят покрытия пешеходных дорожек, обустроят велодорожки, установят площадку для воркаута, поставят сцену, лавочки (link).
киллер is not exactly
юзер is not exactly
воркаут is not exactly
Тренировка sounds more professional - it's like somebody preparing for competition, while "воркаут" has less sport connotations.
This is however about "воркаут" as a noun, there exist (in that sense that it de-facto used sometimes) a verb "воркаутить", however unlike the noun it's a part of only colloquial speech as of now.
So, apart from already suggested "потренирумеся вместе", if you want sound casual and, well, sort of young, you can say something like "может быть, будем воркаутить вместе?" - this is form personally I will never use but it doesn't mean in particular groups it used.
Other option would be to use the verb which stand for actual activity, like "может, будем вместе бегать?" or even "как вы смотрите на то, чтобы приходить заниматься в зал в одно и то же время?".
The last thing I want to add is "потренируемся" is more about a single act, like you are suggesting to do it once, this particular time.