I think people conflate this with the gift given to Winter in Santa Claus is Coming to Town that turns him nice.

I've been watching this every year since about 1969 and I don't recall any mention of a toothache accounting for the Bumbles aggression. It does seem like people have subconsciously made an "Androcles and The Lion" reference on their own in my opinion. I always took his change of temperament as him simply adjusting to a life without his teeth.
He's taking the knife out of the Cheese!
Do you think he wants some cheese?

I remember seeing a Rudolph storybook years ago but I don't think it was a reprint of the 1939 original. The story only featured the other reindeer and Santa Claus. As far as I know, the Bumble Monster is a product of the Rankin-Bass production and was never in the original story.
I was wondering if there ever was a book adapted from the TV special, and if that might have featured a scene with the Bumble having a toothache.

Rudolph first appeared in a 1939 booklet written by Robert L. May, which was later adapted into song, which then became the infamous Christmas special. I've never read it myself, but people swear its mentioned. The odd thing is, after scouring the internet for a good hour and a half, I've stumbled across countless posts from people who bring up the toothache scene. Heck, even a lot of the official merchandise say that Bumble was only mean because of his rotten tooth. I don't take a lot of stock in the whole "Mandella effect" some people have attached to this inquiry, but it's still very strange. How can so many people remember it one particular way? Very odd. Even my friends and girlfriend are stumped by this, as they remember the more
Androcles and the Lion
version and not the one where Hermey goes about making Bumble bald in the mouth lol. Some believe that the scene was broadcast up until sometime in the late 80's to early 90's, and that it still exists on old VHS's, but no one has ever posted any sort of evidence of it.

There's a rather lengthy history of
Rudolph
on the
tvparty.com
site:
http://www.tvparty.com/xmasrudolph.html
It sounds like there have been a few alterations and attempted restorations of this special over the decades. The question of the Bumble's toothache scene has been asked here before, but the question has never been resolved. IMDb just did a housecleaning job on this board so I can't reference the other posts containing this question.
You mentioned a book. Was this special ever novelised or made into a picture-book? It's possible the book contained such a scene and over the years people's memories became blended with those of the film.