I guess my first question is what is it that made you think her parents were Charles and Caroline?I only ask because when I look at the 1900 census I see a Bertha M. Krueger in Weston, Dunn, WI
This is the same County as Menomonie is situated in. She is age 10 daughter of Carl W. Krueger, age 35 and Lena M. age 31.
other children:Anna 9, Clara 7, Frank 6, Walter 5, Alma 1, Minnie 9/12
and with them are August 72, Albina 62 and Rynold 32
all children born WI all others born Germany
I can't find the 1900 census entry for the Charles and Caroline in Wausau that you mentioned.
*** also I found two 1906 census entries for Bertha in Saskatchewan
1906QU'APPELLE, SASKATCHEWAN - townships 4,5, in ranges 7, 8, 9, 10 west of the 2nd M, sub district 9
Bertha, age16, single, servant, born United States of America
1906 QU'APPELLE, SASKATCHEWN - townships 6, 7, 8, 9 in ranges 9, 10 west of the 2nd M
Charles, age 42, born Germany
Lena, age 37, born Germany
Bertha, age 16, daughter, born USA
Annie, age 15, daughter, born USA
Clara , age 14, daughter, born USA
Frank, age 12, son, born USA
Walter, age 11, son, born USA
Alma, age 9, daughter, born USA
Marie, age 7, daughter, born USA
Carl, age 5, son,born USA
Herman, age 2, son, born USA
Henry, age born May, Saskatchewan
August, age 78, father , born Germany
Alabina, age 75, mother, born Germany
Reinhold, age 38, brother, born Germany
all of them are shown as immigrating 1904
there are several other Krueger families on same page from Germany and USA
from these census entries I think that Carl/Charles and Lena are likely parents of your Bertha. They fit with the family found in Dunn County in 1900. I've seen the names Carl and Charles used before for same person so I guess it was common.
The Border crossing database US to Canada only starts in 1908 so too late to find them coming in.
I tried to find births for the children of Charles/Carl and Lena to see what her maiden name - at familysearch.org I found a birth of a Walher August Bernholl Krueger, son of Karl Krueger and Lena Reibs. He was born April 11, 1895 in Weston, Dunn, WI which fits for son Walter and also for where the family was in 1900
also a son Carl Friedrich Wilhelm Krueger, born Aug. 25, 1901 Weston, Dunn
this son is listed in the 1906 census with them - his birth shows parents as Carl Krueger and Liena Reips
I didn't find births for any of the rest of them, but possibly because of spellings ?
I see in 1911 Bertha and husband Henry and daughter Laura (as indexed) are in Assiniboia Sask
Carl and Lena and children are also in Assiniboia district - I can give you the census info if you like. I see that Albertin (Carl's mother is with them, as is his brother Ranhold) Father August must have died.
Hope this helps.