I remember a long time ago seeing the movie Breaking Away, a male teenage coming of age story that involves bicycle racing. There's a scene where the mother tells her son how she has a passport, even though she has never gone out of the country, because that way she is always prepared to travel in case the opportunity arises.* This isn't just a "modern" idea. Our ancestors also traveled and may have applied for a passport. It's another record set that might help you find a female ancestor.
Passports are federal records and as such the National Archives is a great place to learn more.
"The Department of State has issued passports to American citizens traveling abroad since 1789, but did not have sole authority to do so until August 23, 1856, when Congress passed an act (11 Stat. 60) prohibiting other governmental entities, such as state and judicial authorities, from issuing passports."
"Foreign travel in the nineteenth century was much more frequent than one might expect. Overseas travelers included businessmen, the middle class, and naturalized U.S. citizens who returned to their homelands to visit relatives. For example, statistics show that the State Department issued 130,360 passports between 1810 and 1873, more than 369,844 between 1877 and 1909, and more than 1,184,085 between 1912 and 1925."**
Do those numbers surprise you? They surprised me but they are numbers I am grateful for because they mean one more possible place to find a female ancestor or one of her family members (remember, we need to extend our search to include her FAN Club).
Now, it's probably also important to remember that you didn't need a passport for every foreign country. I have American citizen ancestors who lived in Mexico during the early 20th century, but they didn't need a passport. US citizens needing a passport for travel to Mexico or Canada is a more recent law. And you didn't always need a passport to travel abroad. To learn more about passports and when they were required see the National Archive's web page on Passport Applications.
Where, besides NARA, can you find passport applications? One place is Ancestry.com and their database, U.S. Passport Applications, 1795-1925. Additional places are listed below.
Ancestry.com - U.S. Consular Posts, Emergency Passport Applications, 1915-1926
FamilySearch Wiki -United States Passports
FamilySearch - United States Passport Applications, 1795-1925
Department of State - Get Copies of Passport Records (after 1925)
* I'm obviously paraphrasing since I don't remember the actual lines but I remember the sentiment which I wholeheartedly agree with.
**National Archives - Passport Applications
Image citation: "United States Passport Applications, 1795-1925," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:QVJP-3BMN : 16 March 2018), Nellie Bly, 1915; citing Passport Application, Austria, source certificate #1250, Passport Applications, January 2, 1906 - March 31, 1925, 540, NARA microfilm publications M1490 and M1372 (Washington D.C.: National Archives and Records Administration, n.d.).