The calculated distance (air line) between Rüdesheim am Rhein and Bochum is approximately 108 miles respectively 174 kilometers.
By car or train, the actual journey to Bochum is certainly longer, as only the direct route (as the crow flies) between Rüdesheim am Rhein and Bochum has been calculated here.
Air line (approximately)
174 kilometers
94 nautical miles