@bluejets I installed the library using the arduino IDE.
Yesterday I attached a SD card module to the setup to match your TFT/SD combo. I am now at the situation that you are, it does not write the image to the screen.
I am using the "shieldtest.ino" from the st7735 library examples folder, this uses the same "bmpDraw" method that you are using in your original post.
This is what I have seen so far, I can use the library functions to tft.fillScreen(), tft.setTextSize(),tft.setTextColor(), tft.setCursor() and tft.print(). The bmpDraw method prints the following output in the serial monitor
Loading image '/myimage'
File size: 61494
Image offset: 54
Header size: 40
Bit Depth: 24
Image size: 160x128
during this period it sets the boolean "goodBmp" to true.
After all of the above it seems to leave the drawing method without any obvious signs of a problem but not running to completion. So I feel the library is probably fine but this method is not quite right. If I get chance later I might look into the different options, maybe a different function or fix the current function. One very encouraging thing is the fact that the program parses the information at least up until the bitmap data. Printing an image to a tft screen is a common thing so there has to be an alternative method somewhere online.