Yes, it's definitely allowed. We've done it many times. A double burger is too much for any of us, one burger is enough. We split the fries and get an extra cup of ice to split the soda. If it's at the hotel we use our refillable mugs and get a bottle of water with the meal for the room. It works out great.
The cost of the bun changes. I've been given the bun free many times, otherwise it's been no more than $1. I'm surprised to hear someone paid $2, although I would still do that instead of buying a whole other meal.