It is permissible for a married woman to immerse in a mikveh any night when she is
tehorah for
spiritual reasons. In this case, she should not recite a bracha prior to
immersion. She also would not be required to perform the full
preparation procedure.
We are not aware of any classic sources that deal with this question directly, although there are sources explaining why single women (including divorcees) are not generally permitted to immerse.
There is a custom to immerse on erev Yom Kippur for purposes of
teshuvah (repentance). In some communities, unmarried women are also permitted to immerse at this time; a local halachic authority should be consulted.