The 565 image uses 5 bits for the red, 6 bits for the green, and 5 bits for the blue. That is, you're turning your image into a 16 bit color image. The change is visually negligible and the number of bytes to be transferred will still be constant. This is the most compression you're going to get without using ImageIO or writing your own stuff on the other end.
short toSend = ((DataBufferUShort) bufferedImage.getRaster().getDataBuffer()).getData();