Bilirubin is sometimes normal in the urine of male dogs. The way bilirubin is formed in the body is by metabolism of dead red blood cells (RBCs), this is a normal process. As the red blood cells die due to age, the body recycles its products and in the process produces bilirubin, this all happens in the blood. When bilirubin is made the liver than picks it up to be excreted via the feces (stercobilinogen) and urine (urobilinogen).
When we see abnormal elevation of bilirubin in the urine as a result of elevated bilirubin in the blood this is caused by one of 3 scenarios:
1- Destruction of Red Blood Cells is too much and the amount of bilirubin being made is overwhelming the liver.
2- The liver is sick and unable to pick up the bilirubin from the blood.
3- There is an obstruction in the liver that does not allow to eliminate the bilirubin causing a sort of a back flow into the circulation.
The above is a summary of all possible causes of bilirubin production. If your vet has done an abdominal ultrasound and blood work and does not find problems in the liver or evidence of RBC destruction, then the bilirubin in the urine is normal.
If you have additional questions I will be glad to answer them.