I am pretty sure she was actually 28 or 29 when she went missing and that her full name is Gertrude Josephine Bishop, born 21 September 1918 in Albemarle, Virginia. Whilst this is the most obvious match on Ancestry, it is also corroborated at
Full text of "Scarab" which is the alumni publication of the Medical College of Virginia and lists her as a member of the 1940 Class of Nursing with her full name.
There is another odd clue. In Ancestry there is a marriage in 1944 for Gertrude J Bishop to Arthur D Zuckerman in Taylor, Texas. At
Abilene Reporter-News from Abilene, Texas on March 18, 1944 · Page 14 there seems to be a listing of the marriage in the Abilene Reporter, which identifies Gertrude Bishop as coming from Charlottesville. I do not have a sub to newspapers.com so can only read the OCR text. It would be useful if someone with a sub could confirm this reading. If accurate it suggests Gertrude was married (at least in 1944). If it is accurate this is likely to be the Arthur D Zuckerman listed in a 1943 yearbook for.............Medical College of Virginia, on Ancestry.
Ancestry also has records (in City Directories) for Arthur D Zuckerman MD in Manhattan from 1948 to 1953 (he may have been there in other years but not listed in Ancestry). I note the comments about Gertrude regularly heading off to New York and later reappearing. Is it possible she married without her family knowing and was visiting her husband?
I am not 100% sure of the above, but it may offer a bit more to investigate.