The most common and most likely answer to this crossword clue is the 9 letter word EYE-LEVEL
I've seen this crossword clue in Independent
E
Y
E
-
L
E
V
E
L
Buddy explains!
The straight part
We know that "just over the bridge (of the nose)" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case just over the bridge (of the nose) = eye-level.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.