Suppose Clique has a solution. Then there are k nodes that are fully interconnected. After complenting G, there will be no edges between any of those nodes. Delete all (n-k) nodes that were in G but not in the clique. The result is bipartite, so MNDBS is solvable with only k' deletions.
Suppose there is no solution to Clique. That means the maximum clique is smaller than k, so the complement of G will have no independent set as large as k. So the complement of G will still contain edges no matter which (n-k) nodes are deleted from G'. After deleting any (n-k) nodes from G', there will still be at least one pair of nodes from G that are connected and weren't deleted, and there will still be at least one of the new nodes that hasn't been deleted. These three nodes form a 3-clique (a triangle), and so G' must not be bipartite. So there is no solution to MNDBS.