Bill's father is the father of Bill Haverchuck. He is not currently married or even lives with Bill's mother so it is assumed they are either divorced or Bill was born out of wedlock.
The Garage Door:
Upon Neal's accusation that Bill doesn't even have a father, Bill remarks, "I do too!... I saw him three months ago..."
When Bill awakes from his coma, his mother remarks that she has to call Bill's father as "he was worried sick about you."