Unless you have a somewhat obsessive mission to visit every nature reserve and wild place in Dorset you are unlikely to visit Turnerspuddle Heath; indeed you may never even know it exists! There is not much there that you cannot see or hear elsewhere with the notable exception of turtle doves!
If you look for it on an Ordnance Survey map you will see it is named Tonerspuddle Heath but the label on the gate (and the entry on the Dorset County Council web-site) says Turnerspuddle Heath. It is a triangular area, not that large, bounded to the east by the Bovington tank training area and to the south and west by roads. If you do feel moved to visit then try and go at a weekend when the army are not driving tanks around!
Walking across Turnerspuddle Heath I got the feeling that I was the only person ever to do so! That said, the bridle way that you follow was fairly well marked so others must walk or ride that way from time to time. Indeed, I was left to wonder whether T E Lawrence (Lawrence of Arabia) who lived across the road at Clouds Hill, near Bovington, had strolled that way, or even ridden his motorbike along that very same path some eighty years ago? May be I was treading in famous footsteps .... I will never know.