Bilirubin is absent in urine because it is -
Unconjugated bilirubin cannot be excreted in urine because:-

(i) It is lipophilic (lipid soluble) but not water soluble, i.e. it is hydrophobic 
(ii) It is tightly bound to albumin, thus cannot be filtered at glomeruli.
Distributed in the body fat
Conjugated with glucoronide
Not filterable
Lipophilic