Bilirubin is absent in urine because it is -
Distributed in the body fat
Conjugated with glucoronide
Not filterable
Lipophilic
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.