[jjc1]

  How can I turn off the BDP1 display?   Which buttons do I hold down?  Can I set up the display to turn off after a prescribed amount of time?

[srb]

  How can I turn off the BDP1 display?   Which buttons do I hold down?  Can I set up the display to turn off after a prescribed amount of time?

The first place I always check is the Owner's Manual:
http://bryston.com/pages/technical.html
(Can't post direct link because the Bryston URL for the Owner's Manual uses square brackets in the filename and that won't work with forum hyperlinks)
 
Bryston BDP-1 Owner's Manual, Page 2:
DISPLAY BRIGHTNESS & AUTO SHUTOFF
To bring up a brightness and auto shutoff time delay menu, press the UP and LEFT menu navigation buttons in rapid succession. Use the UP and DOWN buttons to switch between setting the brightness (from 1 to 4) and the time delay (from always on, 10 seconds, 1 minute, 5 minutes, etc.) using the LEFT & RIGHT buttons. The menu will dissappear approx. 10 seconds after the last button press.
 
Steve

[jjc1]

  Thanks Steve.  Checking the ownere's manual would have been too easy