Some other things to try:
Boot from the INTERNAL drive.
Connect the USB external.
Go to the Startup Disk preference pane.
Does the external drive show up?
If it doesn't, the Mac doesn't "recognize it" as being bootable.
If it DOES show up, select it and try "restart".
What happens next?
Also, try this:
Power down -- all the way off.
Disconnect the external drive but "keep it close by".
Reboot, hold down the option key to bring up the startup manager.
Once startup manager appears, NOW CONNECT the external drive.
Wait a little bit.
Does it now show up as a bootable option?
Final thought:
How did you CREATE the bootable external drive?
Did you install a "clean copy" of the OS?
Did you clone your internal drive to it (using CarbonCopyCloner)?
How?