Rumor has it that the copyright office has ruled that David Marxsen's version (Uncle Walter) and the Dr Seuss version (Uncle Terwilliger) are distinct songs. The former (which is more recent) has gone into the folk tradition & has been added to by many hands. Here is a compilation I made some years ago after many singing parties:

Waltzing with Bears amalgamated & annotated

s m f   s          D   t    l    s
My Uncle Walter goes waltzing with bears.                        1
s       r   m f s l       s f m
It's a most unbearable state of affairs.
s       m f   s               D       R    M
Every Saturday night he creeps down the back stairs,
M    F   M    R D    s    m    s   l    t    D
Sneaks out of the house and goes waltzing with bears.

         s          m f s       D   t    l    s
       He goes wa-wa-wa wa-wa-wa waltzing with bears.
         R                D R      M R D    s
       Raggy bears, shaggy bears, baggy bears too.
       s               m   f s            D      R    M
       And there's nothing on earth Uncle Walter won't do
         M F M   R D   s    F M R D   s
       So he can go waltzing, wa-wa-wa waltzing,
         M F M   R D   s                  d
       So he can go waltzing, waltzing with bears.

I went to his room in the middle of the night;                   2
I tip-toed inside and I turned on the light.
But to my dismay he was nowhere in sight:
My Uncle Walter goes waltzing at night.

I bought Uncle Walter a new coat to wear,                        3
But when he comes home it's all covered with hair,
And lately I've noticed several new tears.
I'm sure Uncle Walter's been waltzing with bears.

We told Uncle Walter that he should be good,                     4
And do all the things that we said he should,
But we know that he'd rather be out in the woods.
We're afraid that we'll lose Uncle Walter for good.

We begged and we pleaded, "Oh, please won't you stay?"          5
And managed to keep him home just for a day.
But the bears all barged in and they took him away.
Now he's dancing with pandas and he can't understand us,
But the bears all demand at least once dance a day.

We asked Uncle Walter just how it feels                         6
To be light on your feet and kick up your heels,
And he said, "We will see what the music reveals
Tonight when the bears teach us polkas and reels."

That night, when the moon rose, we crept down the stairs;       7
He took me to dance where the bears have their lairs.
We danced in a bear hug with nary a care.
It all feels like flying, there is no denying,
And now my pajamas are covered with hair.

My Aunt Matilda was mad as could be.                            8
"Walter, that rat, never waltzes with me!"
So she took her fur coat and remodeled it so
Now she can go waltzing, and Walter won't know.

       She goes wa-wa-wa wa-wa-wa waltzing with bears.
       Raggy bears, shaggy bears, baggy bears too.
       And there's nothing on earth Aunt Matilda won't do,
       So she can go...
                Waltzing Matilda, Waltzing Matilda,
       So she can go waltzing, waltzing with bears.

I snuck out the back door and over the wall.                     9
The shadows were long, and I'm not very tall.
Then a bear came right over and offered his paw:
Now Walter and I are the belles of the ball.

Said my neighbor Patrick, "Don't crow without cause --          10
Such a queer choice of partners, it must give us pause."
But we waltzed down the alley with never a word:
Pat wears a fur coat, but a bear is preferred.

My uncle Terwilliger waltzes with bears.                         11
Uncle says it's more fun than just sitting in chairs,
And we're not going to stop it. My uncle declares,
"It keeps my mind off of my worries and cares."

My uncle Walter is missing some wares.                           12
He's been that way all his life, mother declares.
It's not that he's violent or falls down the stairs --
It's just that he waltzes, he waltzes with bears.

Verse 1: On Bob Force and Al d'Ossche, "When the Moon Fell on
California".
Chorus and verses 2-5: Copyright (c) 1986 Dale Marxsen, Tomorrow River
Music, P.O. Box 165, Madison WI 53701.
Verse 6: From Gail Rundlett (live concerts).
Verse 7: From Claudia Rose and Grian MacGregor (on Priscilla Herdman,
"Star Dreamer")
Verse 8: From Lui Collins (live concerts)
Verse 9: By Sara Stockwell.
Verse 10: By Joe Fineman.
Verse 11: Remembered by Youngbear from Dr Seuss.
Verse 12: Supplied by Jeff Keller, 30 September 1998.