Quest Talk:Searching for Fresh Springs

Although listed as Fellowship, it is quite possible to solo this by the correct route. Enter the forest NW of Goldberry, head S then E to the Spring; reverse route with the bucket.

For Reference

For reference, here are objectives two and three. Looks like they simplified the quest text.

===Objective 2===

Upon finding the spring that Adso sent you to, you noticed a beautiful but strange-looking woman standing underneath the oak tree on the western bank of the river. Perhaps she possesses the means for you to take water back to Adso's camp.

===Objective 3===

The entrance of the Old Forest lies to the east, and Adso's camp is north from there.

Adso sent you into the Old Forest to fetch water, but empty-handed. Goldberry has given you a bucket in which to carry water back to Adso's camp and has granted you leave to draw from her pool, but warns that the Forest is dangerous.