Law enforcement agents said a tip from someone in Tampa led them to the suspects.
"When you look at this, where the grandmother was willing to sell her own grandchild obviously to some degree for profit, it's appalling," said Wayne Ivey with the Florida Department of Law Enforcement.
Investigators said Bigbee initially wanted $75,000 for the boy, but then lowered the price to $30,000. The child is now in protective custody.
The child's mother is currently incarcerated on unrelated charges.
The Associated Press contributed to this report.