In reply to jon59:
When we did Square Face and Mitre Ridge recently we cycled as far as Fairy Glen, at which point one of my inner tubes exploded and I discovered that my spare was for the wrong bike (oops). So we camped overnight, then walked in the next day. We were making a weekend of it so camped on the plateau, did another route, then walked all the way back out, pushing bikes from Fairy Glen.
Comparing notes with others, it only took us about 15 minutes longer (each way) walking from Fairy Glen to the stream crossing than it would have cycling. And on the return leg, pushing bikes took 40 minutes longer than cycling.