Not a perfect match, but since nothing has been suggested for a few years, I'll give it a try.
This reminded me of Gael Baudino's Dragonsword. It is the first of a trilogy and was published in 1988.
Partial summary from Wikipedia:
Suzanne Helling has been living a nomadic life since she went through the 1970 Kent State shootings, and she winds up in Los Angeles as a teaching assistant to history professor Solomon Braithwaite. Ten years earlier, his marriage ended, and he tried to kill himself. While comatose from his drug overdose, his unconscious mind took flight and created the land of Gryylth, which he patterned subconsciously on 5th-century Roman Britain, in a corner of the cosmos. Though Gryylth bears a superficial similarity to ancient Britain, there are anachronisms: the inhabitants speak modern English; no one remembers more than ten years back; and Gryylth is an incomplete land—it ends in mist and nothingness in the surrounding ocean.
In this realm, Braithwaite has an alternate persona: Dythragor Dragonmaster, the protector of Gryylth and rider of the dragon Silbakor. There he is tall, strong, and a skilled fighter. In the real world, though, he is an old man with a failing heart. Silbakor has been pressuring him to choose a replacement in anticipation of his eventual death. When Braithwaite proves unwilling to choose, Silbakor chooses Suzanne and transports both of them to Gryylth. There, Suzanne also adopts a new persona: Alouzon Dragonmaster, who, like Dythragor, is tall, strong and skilled with weapons.
A new peril faces Gryylth: the Dremords, invaders from the sea, have taken the Tree of Creation from the Blasted Heath and are planning a new invasion. This tree embodies uncontrolled change and chaos, and in the hands of Tireas, the Dremords' magician, it becomes a potent tool for war. While Dythragor and Alouzon clash on their leadership styles, Alouzon also realizes that Braithwaite's biases have colored Gryylth: the Dremords are unquestioningly feared as enemies; women are little more than chattel unable to bear weapons in their own defense; and magic is feared and distrusted.
Points for it:
- Female author
- By late 90s it was 10 years old
- Woman from America sent to fantasy world
- She travels with her professor
- Fighting invaders of the land
Things that don't match:
- Not an archer, but could be good with a bow
- Not Norse & no Odin or Thor but 5th century Britain
- No Robin Hood in the sequel