Is ecological bin packing NP-hard?
Yes, this can be solved in polynomial time, for arbitrary $N$.  This is an instance of the assignment problem, for which polynomial-time algorithms are known.

You want to assign a color of glass to each bin, such that each bin gets exactly one color, and each color is assigned to exactly one bin.  The cost of assigning bin $b$ to color $c$ is the number of bottle moves needed to move all bottles of color $c$ that aren't currently in bin $b$, into bin $b$.  Therefore, this is an assignment problem.

(You can compute this cost function more efficiently as follows: the cost of assigning bin $b$ to color $c$ is the number of moves needed to move all bottles that aren't colour $c$ out of bin $b$.  Thanks to @David Richerby for this insight.)

The assignment problem can be solved using standard methods, e.g., the Hungarian algorithm or algorithms for min cost max flow.