I think the answer might be
Take the blackest of pits that yearns for the light
I think this is eye as suggested by other answers and the first hint (the black pit being the pupil)
See the fruit that it has for distance and night
Looking at the second hint I think this must be grape (recent research has suggested that grapes help keep your eyes healthy).
Now warp the fruit's name and turn up the bass
A possible anagram of grape is pager.
Turning up the bass could be suggesting wordplay involving literally turning the first letter up (i.e, 'p' becomes 'b') to get bager.
And what is the answer you pull from this chase?
There's an extra g I'm putting in here which I cannot explain other than to say bager sort of looks like bagger but there are other reasons why this might work.
For example, in baseball, a double bagger is a hit which allows the batter to immediately run to second base, so we get the idea of chasing the bases and the link with the word 'bass' in the previous line.
A triple bagger, in baseball, is a hit which allows the batter to run to third base.
The batter's eye is a solid-coloured area beyond the center field wall of a baseball stadium, that is the visual backdrop directly in the line of sight of a baseball batter, while facing the pitcher and awaiting a pitch