Your timing is going to be too critical to make bit banging, which is what you are attempting to do, likely to work with just a loop.
Have you looked at the SoftSerial liburary.
Having said that I think both chips have UART's that is Universal Asynchronous Recieve and Tansmit hardware.
you should be able to set them up at the same board rate and just read and right to the buffers.
If you look at the data-sheets to find the functionality and then search for how to implement it in your IDE you should find what you need.
I am pretty sure the Arduino IDE will do most of the work for you, at least at one end.