Google's not working for me anymore at Malheur NWR. Seems that Princeton is too small to be on their radar. They take me to Princeton NJ!
If you type in 97721 into Amtrak's station search tool you'll come to their Google map. Shows the bus connection at Burns. Here's a screen shot. You'll have to go to that page on your own to scroll in and out. I can't seem to link it...
Take above mileages with a grain of salt. They say 118 to Winnemucca NV whereas Google Maps says 183. GM also says only 38 miles Princeton to Burns.
If Google Maps is your preferred interface and you know now that you want to end your trip at Burns OR, you no longer need the Google Amtrak search function. Just search for bus depot at 230 Hines Blvd (Reid's Country Store). Google will certainly find that. Or zoom in on the above.