Couple of things. When trying to burn the bootloader, make sure that its definately trying to communicate by disconnecting the board from the TinyUSB. It would give a different error message.
When you click 'Burn the bootloader' THEN press the reset button. Also, double check the pin out connections and make sure they match up. (I.e. RX goes to RX, TXD goes to TXD etc.)
If that fails, try it all with power to the board (Connect the PSU-ON to ground) and try all the above steps. You will know when it works, as the red debug light will go flash-flash-flash-pause-flash. Or similar, not quite sure now!)