I was wondering that too, considering her car is presumably parked less than a block away for her to stash her clothes in, then all she'd need to take with her is her car key.
We've been told her clothes are stuffed in the bag - we've also been told that the ride is not the task - that might well mean she's going to change back into her clothes when they get there.
It would feel like a missed opportunity, having Sophia in form-fitting leather and not building the scene around it, but I'm also assuming Aiden tells her to keep them afterwards - meaning they could make a reappearance later on.
It is a small detail but it actually poses an interesting question, beside my previous half-joke about the safety.
As you said all she needed was the car key and maybe the phone.
So it is likely that for the real task she has to change back in her clothes and then back in the suit, unless the trip back happens on a different mean of transportation, like a train/bus or someone giving him a lift back.
Considering what you said and we know about the suit, if she gets to keep it, that could also mean a recurring task, i.e. it won't be the last time they go for a ride and/or get to this place to perform similar tasks, one more challenging that the previous one.
I think that taking her away from the city means that, whatever the task is, Sophia won't be concerned about being recognized. In the voyeuristic scenario, as many have suggested so far, this will lead to some kind of exposure of Sophia. This PD seems to have a theme for Sophia's breasts (in any event of the current update she showed them) so that could be it, but imo in this scenario is a bit too early for that kind of public display (considering the pace of the game etc etc).
I think there could be another scenario different than the voyeuristic one, but it is really difficult to imagine one as we still don't fully know Aiden's angle, what his purpose is with the tasks. The voyeurism fit for his thirst for bullying and humiliating the "authority", like the first 2 tasks. But there could be more maybe.