Bamiyan is regarded as one of the safer destinations in Afghanistan. Its remoteness and the largely Hazara population have kept it distant from most of the action.
The southern route to Kabul is considered dangerous for the hour or so stretch just out of Kabul where it travels through several villages. Most public transport takes this route, so keep a low profile in those areas and cover your head with a scarf as the Afghans do.
There are many landmines and unexploded ordinances UXO in Bamiyan despite a continued presence by ISAF. Stay on well used paths and steer well clear of red-painted rocks. White-painted rocks indicate paths that have been cleared of mines.