IOS only talks to Bluetooth 4, known as BLE, so that is what you need. A typical example is the HM-10 but I understand it is rather limited in its capabilities and, depending on what you want to do, you may need something fancier. Similarly, you may need to check what is available to use on the phone.
Some useful information here HM-10 Bluetooth 4 BLE Modules | Martyn Currey