I could not find a software using plain Bluetooth 4.0 with iOS devices. But there is a good BLE (Bluetooth Low Energy) controller from DFRobot out there. The communication is a little more complicated than the plain strait forward Serial interface with just 2 defined pins for RX and TX and the connection speed, but I made it work: Project ESP32.
Arduino robot with Bluetooth 4.0 control
Since iOS only supports Bluetooth from 4.0 on and the HC-05 module is Bluetooth 2.0 we needed to upgrade our first model T-100 with a different Bluetooth module: Now we use AT-09. Then we can use our iPhones to control it!
How to build a robot in 30 seconds: https://www.youtube.com/watch?v=4jvJJgrxoKo.
More details in the Wiki.