How do I get the printer to print automatically using the bypass tray

You can set the bypass tray the size you want then set paper size setting in the printer driver at your PC.

Hold down the [PAPER SIZE ENTER] key more than 5 seconds to
set the selected paper size.
The currently selected paper feed location indicator will blink and the
corresponding paper size (which is currently set) indicator will light
steadily.

All other indicators will go out.
If the machine has two paper trays, use the [TRAY SELECT] key to
select the paper tray for which you wish to change the paper size
setting.

Each time the [TRAY SELECT] key is pressed, a paper tray will be
indicated with a blinking paper feed location indicator.
Use the [ORIGINAL SIZE ENTER] key to select the paper size you want to set.
The indicator of the selected paper size lights up.

Press the [START] key and then the [PAPER SIZE ENTER] key.
To change the paper size setting of another tray, repeat steps
after pressing the [START] key

Make sure that the tray's paper size setting is the same as the tray's
paper size setting in the printer driver. For example, if the tray's paper
size setting is A4R (LT-R), set "Setting Paper Size" to "A4-R".