The dog wouldn't have ____ the postman.
first of all the tense is in the past perfect tense which is clear by would not have which express this tense and that the verb following by the word have it should be in the past participle
Tom, would have + past participle is not the past perfect. Had + past participle is the past perfect.
As for the choice between 'bit' and 'bitten', I prefer the old-fashioned 'bitten'. I'd love to know to what extent the preference is regional. I'm an American and prefer 'has bitten,' 'has gotten,' 'has proven,' and so on. The opinions of American acquaintances of mine vary, as do the opinions of British acquaintances.
The first paragraph of my post has gotten lost.
The question uses the subjunctive pluperfect.