In the caption she also suggested Bing had finally been building a relationship with their son Damian, who Bing initially denied was his child until it was proven by a DNA test.
"In the past year we had become close again. We last spoke on our son's 18th birthday."
Damian also shared a tribute to his father on Instagram.
"Thank you from the bottom of my heart to everyone that has reached out following the devastating news," he wrote, alongside a photo of a red sky.
"This is a very strange and confusing time and I'm immensely grateful to be surrounded by my phenomenal family and friends."
The movie mogul died by suicide at the age of 55, it is being reported.
TMZ reports that Bing, who wrote the comedy film Kangaroo Jack in 2003 and later invested nearly $US100 million in the animated hit Polar Express, died at his luxury apartment building in LA's Century City neighbourhood.
The outlet quotes sources close to Bing as saying he had been depressed about being isolating in quarantine during the coronavirus pandemic.
Bing became a Hollywood power player after inheriting $US600 million from his grandfather on his 18th birthday, dropping out of college and using the money to found his own company, Shangri-La Entertainment.
His credits as an executive producer include Get Carter (2000), Looking for Comedy in the Muslim World (2005), Youth in Revolt (2009) and Rock the Kasbah (2015).
He is survived by Hurley and his other child, daughter Kira Bonder, who he had with tennis player Lisa Bonder.
Last year it was reported that Damian, 18, could stand to inherit nothing of his father's vast fortune amid a nasty legal battle with his biological grandfather.
The bulk of Bing's fortune came from his grandfather, New York real estate baron Leo S. Bing.
Hurley's grandfather, Dr Peter Bing, last year argued that Damian and his dad had never met, and that the teen isn't eligible to become a Bing heir as he was "born out of wedlock".
WHERE TO GET HELP:
If you are worried about your or someone else's mental health, the best place to get help is your GP or local mental health provider. However, if you or someone else is in danger or endangering others, call police immediately on 111.
OR IF YOU NEED TO TALK TO SOMEONE ELSE:
• 0800 543 354 (0800 LIFELINE) or free text 4357 (HELP) (available 24/7)
• https://www.lifeline.org.nz/services/suicide-crisis-helpline
• YOUTHLINE: 0800 376 633
• NEED TO TALK? Free call or text 1737 (available 24/7)
• KIDSLINE: 0800 543 754 (available 24/7)
• WHATSUP: 0800 942 8787 (1pm to 11pm)
• DEPRESSION HELPLINE: 0800 111 757 or TEXT 4202
