If you're seeing BMP+ZIP being smaller than PNG it only means your PNG encoder is poor. This can be easily fixed with a PNG optimizer like Zopfli, AdvPNG or OptiPNG.
https://github.com/ajslater/picopt ...will do this automatically for you.
Pictopt: A multi-format, recursive, multiprocessor aware, command line image optimizer utility that uses external tools to do the optimizing.
For an all in one GUI for Mac approach to this, try ImageOptim
http://www.olegkikin.com/png_optimizers/
1_zopflipng.png 8.466 2_zopflipng.png 18.739 3_zopflipng.png 8.012 4_zopflipng.png 91.879 5_zopflipng.png 1.117