Damian, 18, wrote on Instagram that it is a “strange and confusing time” as he processes his father’s death.
Bing and Hurley, 55, met in 2000 and had their son Damian in 2002.
Sharing his gratitude for messages of support, Damian wrote on Instagram: “Thank you from the bottom of my heart to everyone that has reached out following the devastating news,” he said.
“I’m trying to reply to as many of you as I can, but please know I will always remember your kindness. This is a very strange and confusing time and I’m immensely grateful to be surrounded by my phenomenal family and friends.”
US reports state Bing died after falling from a building in Los Angeles. His publicist Michella Bega confirmed the news to Sky, stating she was “overwhelmed trying to process this unbelievable and sad event.”
Damian’s post follows his mother’s own tribute to Bing, as the model and businesswoman shared a series of old photos from when they were together.
“I am saddened beyond belief that my ex Steve is no longer with us. It is a terrible end,” she wrote.
“Our time together was very happy and I’m posting these pictures because although we went through some tough times, it’s the good, wonderful memories of a sweet, kind man that matter.
“In the past year we had become close again. We last spoke on our son’s 18th birthday. This is devastating news and I thank everyone for their lovely messages.”
Bing was a film producer who co-wrote the 2003 comedy Kangaroo Jack and also helped finance the 2004 animated film The Polar Express, starring Tom Hanks.
He produced the 2000 remake of Get Carter, starring Sylvester Stallone, and Martin Scorsese’s Rolling Stones documentary Shine A Light.
Bing also founded Shangri-La Entertainment, a company with interests in property, construction, entertainment and music.
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With additional reporting by Press Association