Chris, Chambers of course uses phonetic symbols that questioners here might well be unfamiliar with to indicate sounds. So that there would be no confusion here, I wrote it (the 'n' + *upside-down 'e' + s) as 'niss', though I might equally have written it as 'nuss' or even 'ness', I suppose. My point was to indicate that there was no 'ow' sound which someone might easily assume with the letter-sequence 'nous'. Indeed, the very word 'nous', meaning common sense, is thus pronounced! Surely 'bound' does have an 'ow' sound, too...at least it does the way I say it! That would surely give hay-nowce.
As regards the two possible pronunciations, I'm sure Chambers has simply taken on board the fact that people do nowadays pronounce the word in both these ways. My edition was produced in 2003, whereas my version of The Oxford English Dictionary - which agrees with you about the single pronunciation - dates from the 1980s. Things change in twenty years.
* The upside-down 'e' is pronounced like the 'a' in 'another', but I felt writing it as 'a' would simply have made things even more difficult.
But what the hey! Cheers