Mens bueche girod 9k gold watch the gold band is 1 inch short

You have two options and for both you need to find yewellery repair shop.
Option1) Some jewellers sell NOS (New Old Stock) gold watch bands. If your vallet is thick enough for this option- shop around and buy one.
Same jewellery repair shop will be able replace the old band with the new one, even if the band is soldered to watch case.
Option2) In the same shop ask if they can built up (lengthen) the clasp. In this case you will spend less money, but you will loose on looks.
Note: As mostly all gold watch bands are maschine made, it is allmost impossible to repair or lengthen them in a good looking way. Anyway- consult the jeweller first and see what he says. He may have some NOS witch is exactly matching your old watch band pattern.
Good luck.