It should check if its in your inventory and turn it into a trout instead of giving you another one. it checks for notes and the bottle so not sure what's gone wrong there
A full set of what I did, in case it helps with finding the cause.
Talked with King and received the quest.
Bought Net 3 and fished up a bottle
Broke bottle without talking to the king again, which ended up with a dialogue option of "I got the bottle open" without an interim "I got the bottle" or something similar.
Tried like 15 different words and shelved the quest
fished for an extended period of time (15 minutes or so) and obtained 3 additional bottles.