If they didn't chew, they wouldn't have to wear The Bucket.

When I met my dog she had a bucket on her head - cos she'd been desexed and obviously wanted to chew. Cos it had been two weeks, they took the bucket off her when I adopted her, but she still wanted to chew so I put aloe vera (tastes yukky) on the wound and that slowed her down.

They can be very sneaky chewers especially if you stop them when they do and deep healing wounds are VERY ITCHY - I can vouch for that personally. Worse than mozzie bites.

Dog spit is good but chewing is bad.

So I would treat the bucket like a muzzle or head halti. They're not going to like it if you don't pair the wearing of it with a fun game of eat roast chicken or raw beef mince or similar.

sniff the collar - get a treat (through the collar)
put head through collar - get lots of treats
wearing collar - get lots of treats.

Nothing like really yummy treat to help distraction of the itchies. And if you can put something cooling on the wound like aloe vera or ice (wrapped up) that will help too.