I don't think you're being unreasonable in the slightest.
Sure, there are some people who would go "Oh hey, you invited Bossypants? Great, I was thinking more people would make it more fun!" But that's certainly not everybody.
I've told this story before on here before, but once, I invited a friend on a shopping trip to spend a gift card. She invited another person to come along, and I rolled with it because "the more, the merrier," right? Not so much. After trying to change the day, the time and the city where we were going to shop (unsuccessfully, tyvm), (Un)invitedGal pouted, sighed, grouched and moaned through the whole afternoon, only cheering up after I offered to drive to and pay for dinner. No merrier about it.
Let her know that if she wants to camp with Bossypants, that's fine, but since you were planning on this being a trip for just the two of you, you're going to just bow out and let them have their 'special thing,' and the two of you can hang out another time. (aka, what doodlemoor said)