Miami Beach police released the recording on Tuesday.
Police say 41-year-old Chautele Cooksey collapsed at Bosh's home last week and later died at a hospital.
On the recording, Bosh tells the operator that Cooksey is having trouble breathing and that she needs an ambulance. He calmly tells the operator that Cooksey has passed out a couple of times but regained consciousness. After a few minutes, Bosh's wife, Adrienne, takes over and begins to express concern at Cooksey's worsening condition.
Police say they're conducting a standard death investigation, but no foul play was suspected.
A police report says a friend of the victim told officials she had survived cancer about a year ago.