Hi KG!
There must be a form of telepathy going on here, because I've also been perusing the Anaconda/Butte city directories for the periods when Bridget was living there also.
Here's what I have, starting with 1896. (my bold/italics indicate who may be our Bridget):
Butte:
1896: Bridget Sullivan, seamstress
Mrs. Bridget Sullivan, E. Daly, Walkerville
Bridget Sullivan, domestic, ss O'Neill, 6 e of Main, Centerville
1899:
Bridget Sullivan, dom., R.F. Pearce
https://familysearch.org/ark:/61903/1:1:MM58-TMX
Richard F. Pearce was a manager of the Colorado Smelting & Mining Co. in Butte. Considering Bridget married a smelter man, this may be significant.
Bridget Sullivan, dom., rear 123 Dublin
Bridget Sullivan, dom. 201 Dublin
Bridget Sullivan, dressmakr., b. 314 E. Woolman
Bridgie A. Sullivan, conf., 930 N. Main, Centerville
1900:
Bridget Sullivan, dom. R. Pearce
Miss Bridget A. Sullivan, conf., 930 N. Main, Centerville, r. same.
Anaconda
1902:
Bridget Sullivan, dom, 610 Hickory, Frank Norbeck, Asst. Cashier of the Daly Bank & Trust of Anaconda.
1905:
Bridget Sullivan, dom., 522 Locust (family of William & Maude Johnson?)
Bridget Sullivan, dom., 510 Main (G. Winston)
1905 Bridget married m. John M. Sullivan
1910 residence 412 Monroe St.
1916 residence 701 Alder
1939 Bridget Sullivan (wid. John M.) h. 701 Alder
1942 Mrs. Bridget Sullivan, 112 E. Woolman
1945 Sullivan, Mary (wid. Of Timothy) h. 112 E. Woolman (Bridget is not listed as a resident at this address)
Bridget Sullivan, h. 322 W. Bway, apt. 5
Bridget Sullivan (wid. M.H.) h. 920 W. Copper
Bridget Sullivan (w. John T.) h. 415 Pennsylvania Ave.(This Bridget Sullivan died in 1947; her parents were Bart Harrington & Johanna Kelly).