Yes you can get into Stonehenge and also into Avebury.
Neither will permit bikes to be taken in, you will have to lock them to a flimsy barb wire fence nearby.
Personally, I would rather lop off my right ear.
The night will be full of drunken doped up twits and they will not steal your bike, but they may piss on it and or sit on it and or generally destroy it because they are ignorant.
No lighting of any real value and the cops will do nothing as there will be no witnesses to anything.
Personally, I would go to Avebury. Much nice, much more friendly, much more free and easy, less f'wits, less agro.