I was pulling my hair out over this one too. Here's the solution that started my 6510 printing from Tray 1 again. My paper size setting was incorrect for Tray 1. Setting it to 8.5 x 11 was the solution.
For what it's worth (not much, I know!) I am having the same problem. It started after I had cleared a paper jam.
I've been trying to fix it for the last 3 hours.
Even printing the printer config pages via the Menu on the printer result in the same error.
I have tried every setting you can think off this printer since new has always done this straight out of the box, every time I print I get this error Add paper-bypass tray. Every time I turn the printer off (power down) and try a print if gives me the same error. I have upgraded to the latest firmware thinking this would fix it but it still does the same. There are no settings I can find that are asking for a print to the output tray all setting are pointing to tray 1. Any help gratefully received we have had this printer for months but are unable to use it due to this error. Is there a way we can even disable the output tray ? Or any way to get this printer to print from the normal A4 print tray 1. I only have 1 main print tray and don not have Tray 2, Optional 550-Sheet Feeder. In the menu there is only an option for tray 1, but the printer seems unable to print to it always sending prints to the By-pass tray even though the tray is not selected and is closed.