Encrypting small packets with low data rate
in general, a widely used algorithm to exchange/set up session keys is Diffie Hellman. While exchanging public keys, during the process a shared key is generated, that could also be used to encrypt the communication, without additonal AES. 

I do not know how deep your knowledge of asymmetric encryption is- generally, there are two(three) problems that are used. None of them are trivial- factorisation, discrete logarithms and elliptic curves, the latter often combined with the first two.

However, I'm missing out some details that would help- would you rather have a fast encryption (because in that case I would recommend an elliptic-curve based Diffie Hellman, as ECDH) or an easy implementation (standard DH). Is it important that the algorithm is CCA secure(DH is not). How high shall the security be- how much computation power do you have? Can the key of the IPhone change, or should it always be the same? It would also be helpful to know what kind of bluetooth device it is. 

Another approach would be using one-time keys. The communication could be initiated by the bluetooth device, which has a storage of several keys that may only be used once- in this case to encrypt the session key. 

Last but not least, CTR mode is considered less secure than other cipher modes of AES. Personally, I would recommend GCM for you- because I like it, and because it also provides authenticated encryption, and can be pipelined easily. It has a 128 bit block size. If you expect many errors, OFB could be useful for you... but that goes too far. If you clarify your question a bit more as I‘ve indicated, I can help you out further.