Is it possible for elevated bilirubin levels and being vitamin d deficiency to have anything to do with each other?

Doubtful: I highly doubt any relationship between elevated bilirubin and vitamin D deficiency in adults. Given the epidemic of vitamin D deficiency, physicians would see thousands more patients with elevated bilirubin if there was a relationship between the two. That being said, a 2013 study from Asia suggests low vitamin D may be associated with elevated bilirubin in neonates.