I could have been your friend A.
First and foremost: Please don't lie about this to A. That can hurt so much more than it does good in this situation.
I have experienced these situations and am experiencing them still. Some of my friends have started to become friends with others, with whom I don't (and in some cases do now!) have a connection. It felt like those outsiders were stealing my friends.
It also happened that they had events together, where I wasn't invited. I understood that, because we all have other friends. However, when these were hid from me, that hurt. But I noticed that they were not hid from me intentionally. That took some time to realize, but it helped me understand that my friends have other friends and it's not a big deal. I now invest more time in 1 to 1 contact with some of my friends, and some of them do the same. (And a few of them are just not the ones for 1 on 1 contact.)
Let's break down the situation. This is what the three players want:
You: Join trip with B, without upsetting A, or losing trust of B
B: Join trip with you, avoiding conflict with A
A: Maintain friendship with you
And as a sidenote: A is unaware of this situation, but might (very likely) become aware.
This is a dilemma
Because the only way for B to avoid conflict, and you to not lose B's trust is by lying to A.
That's a very high risk and could do much more damage than being honest would. You already mention yourself that yu do not feel comfortable doing this. I just want to emphasize this even more. Consider the opposite: your friend doesn't invite you to a 1 on 1 event with a random other friend. Would you be upset? Probably not. And if they did everything in the world to cover it up, until you see the photos on Facebook?
So, we cannot get a perfect score in this dilemma. But I think we can get a very high score.
Besides lying to A about your weekend plans, another BAD option would be:
-Not going on the trip: failing both your demands and B's demands. It would be overreaction, too.
They are both bad because they are based on assumptions you make about how A would react.
The only thing A wants in this dilemma is to be friends with you and feel that way.
Since lying is not an option, A should become aware of the trip.
This could be after the trip. But I would recommend doing it on beforehand. For you, to not feel awkward about the situation. And for A, because it's a key turning point in how long you are holding back information. The later they become aware, the more painful it can be. Personally, I would think: They already went on that trip? We must have seen each other at least 10 times before they made plans, how did I not hear about this?
So how to do this:
Don't sit down to have a "good" conversation about this with A. Mention it briefly, but don't talk over it or change the topic of the conversation quickly. Make sure it lands.
You know A best, but I would say something like this during your regular get-together:
[related topic] is something B and will probably do next weekend. We're going to check out [location of visit], the two of us. Should be fun.
If you feel it's necessary then show that you realize that A might feel left out or share your (true) intentions of also doing something like that with A, but do not make this bigger than it is. Trust that they will understand that you can have fun with others, too. Just emphasize that A is also your friend and consider spending some quality time with them, too.
For me, knowing that my friend has 1 on 1 events both with someone else, but with me too, makes me consider them a better friend than a person who has none of these events.
For your relationship with friend B, I reference the answer by Jesse: you are not responsible to avoid awkward situations between A and B. It's not your problem. That is, unless you lie to A. But I do think that you can be the solution. And I don't think B HAS to pay the highest price because they are the "biggest jerk" (from a perspective you draw).
Here, I would be clear to B, whenever he next asks you to hide this from A:
Look, A is my friend and I'm not going to lie to him. I won't make a big deal about is, but if they ask about i'm just going to say we're going to have fun next weekend, the two of us. I'm sure they'll understand.
Let's go back to the dilemma:
All outcomes are met, except conflict aversion of B to A (indirectly).
And the trust of B to you.
I think that these prices are much lower than that of losing a friendship.
I didn't mention the Aspergers. That's because I don't think it changes the situation. As you mention, it could be why B has difficulty being around A, and therefore the reason that this dilemma started. For the solution, just be clear that the points you want to make are received. A will hopefully realize that you are their friend and this situation doesn't change that.
You didn't mention if A wants to be friends with B. I don't think that's possible if B feels so strongly about A. But it's also not your concern. It would prevent these dilemma's, but if it's not there then it's not there.