The calculated distance (air line) between Mazār-e Sharīf and Bāmyān is approximately 136 miles respectively 220 kilometers.
By car or train, the actual journey to Bāmyān is certainly longer, as only the direct route (as the crow flies) between Mazār-e Sharīf and Bāmyān has been calculated here.
Air line (approximately)
220 kilometers
119 nautical miles