Yes, a regular mop can be used to clean bamboo flooring. The mop must be wrung out and should be damp rather than wet. If the mop is wet, there is a danger that the excess water may which is left on the surface of the floor may find its way in between the joints and cause water damage to your bamboo flooring. Water damage would cause your floor to warp, distort and change colour.
Never use a steam to clean a bamboo floor as the temperature and water vapours can penetrate into the flooring, causing irreparable damage.