Usually, I avoid these kinds of threads. They seem not to be that
... But what the hell, I have time on my hand, at the moment, and avoiding questions is never an answer.
So, here are my limping thoughts, pure specualtions:
I am sure that BJJ is like any martial art: people having fun together in training, enjoying their mutual improvements, and exploring the intricate "chess game" of friendly battle. So, no reason to immediately assume the need for self defense brutality. I prefer to think of it as something in the dojo, and not in the street. Most martial artists don't pick fights in streets.
So, in the dojo, then:
To me, BJJ is a lot like judo's newaza, ground work. Skilled judoka are very good at it, because they practice it a lot. BJJ athletes, too, maybe even more so, since that's about all they do.
A weakness of aikido, in comparison, is that we practice so much - standing, seated, weapons, several attackers, all kinds of attacks... We cannot be as skilled on any of those parts, as somebody can when specializing.
Therefore, the aikidoka should try not to get down on ground, but stay up, where the BJJ athelete is not as trained. Of course, that's easier said than done
Also, the techniques applied should be those applicable at a bigger distance than the one normal to grappling - a wrist technique on an extended hand, and so on. The timing should be early, not waiting for any kind of clinch.
And one should be very wary about trying a seated pinning. It is very difficult to pin a judoka, and surely also a BJJ athlete. On the other hand, we hardly practice standing-up pinnings at all.
Maybe the best strategy would be standing-up throwing techniques only, until the class is over? Such as kotegaeshi, and kokyunage on a sankyo grip, and other throws that are initiated at a distance on an extended arm.
Occasionally, we do some suwari-sumo, newaza, or what you want to call it, in my dojo. I try to find the aiki way of doing it, and find it to be very rewarding training, indeed. I recommend it. Aikido is a set of principles, not certain techniques or fighting forms, so these principles can be applied to any style of martial art, modifying it - and, I would like to think, improving it.
Generally speaking, there is no martial art so superior that a beginner of it can defeat an advanced practicioner of another art. So, the one who is the best at his or her art will most probably succeed.