Bathrooms, Machu Picchu
Quite simply, there aren't any.
You'll quickly lose your inhibitions about relieving yourself in the great outdoors, because you won't really have a choice when necessity calls. The trek group with whom we went, provided a small tent which we referred to as the "crapper" as much for its smell as for its so called utility. I refused to go anywhere NEAR that thing - believe me, the "natural" alternative will win you over too!
But beware - one of the members of our little group suddenly felt the urge to go, and we happened to be crossing a rather narrow path along the side of the mountain. He waited until we all passed him and indicated he'd catch up to us when he'd finished his business. Then, as he dropped his pants and squatted by the side of the trail, he heard the sound of running footsteps approaching. He was caught "en flagrante delicto" - nothing he could do but smile at the porters as they ran by him with our backpacks and the group tents!
Can you imagine how embarassing that must have been??!!!
So just be careful where you go - and when!
Outside the actual Machu Picchu national park, there are a few tourist amenities. Flushing toilet is available. However, you have to pay one sol. So make sure you carry some changes at all time because changes are hard to come by in the middle of nowhere.