Maybe the story you are looking for is
Evolution (rated MA) by
sarhea. It's a relatively short story, but very well written. It is also complete with 6 chapters.
The scene you are describing is not the same, but the aspects of Kagome mimicking Sesshoumaru's powers are similar. She also takes on some of his characteristics that she agrees with, like his loyalty, pack mentality, honor, and control of one oneself, power or otherwise.
This happens in the third chapter of the story, although Sesshoumaru finds Kagome not by the well, but inside a cave within a cocoon during the previous chapter. He stays around because he finds the aura emitting from Kagome calming and soothing.