Bryan Randall died aged 57 after being diagnosed three years ago with amyotrophic lateral sclerosis (ALS).
In a statement, Randall's family said they were "immensely grateful to the tireless doctors who navigated the landscape of this illness".
Bullock was also praised for her care by her sister Gesine Bullock-Brado in a tribute she posted on Instagram.
"ALS is a cruel disease," she wrote, "but there is some comfort in knowing he had the best of caretakers in my amazing sister and the band of nurses she assembled who helped her look after him in their home."
