To show dogs do they need to have all their bits and pieces?

The standard on most if not all the breeds state
must have 2 healthy testicles.

A bitch could be shown if spayed as there are no outward signs
but ideally all are shown entire.

I have successfully shown two speyed bitches............

Ideally, yes, though it's perfectly possible to show neutered animals provided the KC has been informed. Castrated dogs are less likely to do well than entire dogs (unless it's known that he's already sired progeny), because the standards say that 'all dogs should have two apparently normal testicles fully descended in the scrotum'. A spayed bitch is much harder to detect!