I have been camping= you have been on a camping trip and have returned Example: How was your holiday? I have been camping up in the Blue Mountains and it was very cold.
I have gone camping= You are still camping and have not returned OR you have gone camping before[ previously on another occasion]. Yes I have gone camping before but I didn't like it.
Also you could write a note for someone: Don't worry about me, I have gone camping and will return next week.