The Mishna in Niddah 8:3 records a case of a woman coming to ask Rebbi Akiva a niddah shailah.
מעשה באשה אחת שבאת לפני רבי עקיבא, אמרה לו, ראיתי כתם.
אמר לה, שמא מכה היתה ביך.
אמרה לו, הן, וחיתה.
אמר לה, שמא יכולה להגלע ולהוציא דם.
אמרה לו, הן.
וטהרה רבי עקיבא.
This implies that the woman can go, although it's always possible that she wasn't married and was asking Rebbi Akiva for teruma and kodshim purposes, so there was no husband to ask.
On [g Niddah 20b, there is the story of Yalta asking her Niddah question to two Rabbis, one of whom she reports to have asked on a regular basis:
ילתא אייתא דמא לקמיה דרבה בר בר חנה וטמי לה הדר אייתא לקמיה דרב יצחק בריה דרב יהודה ודכי לה והיכי עביד הכי והתניא חכם שטימא אין חברו רשאי לטהר אסר אין חבירו רשאי להתיר מעיקרא טמויי הוה מטמי לה כיון דא"ל דכל יומא הוה מדכי לי כי האי גונא והאידנא הוא דחש בעיניה דכי לה
Yalta brought a blood stain before Rabba Bar Bar Chana, and he pronounced her impure. She subsequently brought it before Rav Yitzchok son of Rav Yehuda and he pronounced her pure.... She told him "Every day he pronounced this type of blood to be pure..."
The Rishonim all assume that Yalta was married to Rav Nachman at the time of this account, and yet she went to ask and not her husband. Some of the Rishonim (for unrelated reasons) suggest that her husband was out of town when this happened, but this happened frequently, as she attests.
R' Yosef Berger in Ner Israel has a special "shailah" box under his mailbox where people can drop off their bedikas if it's late at night, so in that Kehillah it is often neither the man or the woman presenting it.