Ever been on a small boat on a fast moving stream? Like that.
Ever driven a 4wd over rough terrain? Like that.
On some days it is as smooth as any multi lane highway, other days it is bumpy.
The small aeroplane is designed to handle it just fine.
With regards to your fear of heights it isn't a problem. With cliffs, tall buildings and the like you have a physical connection drawing your vision down to the ground. With an aeroplane you don't. Hence you don't usually get the feeling of vertigo. You'll find many pilots learn to fly to over come their fear of heights.
