There are two issues here:
The first is that Apple does have the right, as does any retailer to decide if they wish to carry a product in their store. This in itself is not objectionable, what makes the situation highly objectionable in the Apple case is that Apple uses DRM to prevent an application that is not obtained from their store from being installed on devices they have already sold to end users. This turns the normal actions of a retailer in choosing to carry a product or not into an act of censorship. Furthermore in many situations regardless of whether Apple chooses to approve or to not approve an application, Apple will always be in the wrong. This by the way does not apply only to Apple it equally applies for example to Microsoft’s Windows 8 on ARM or to a locked game console for example.
The second is very specific to Bitcoin and is in fact a very critical threat to the viability of Bitcoin. The security and viability of Bitcoin is totally dependent on the complete control of computers and devices by their respective owners. If one allows a situation where a single corporation or a group of corporations can control a majority of nodes or a majority of the hashing power, by the use of DRM locked computers or devices as is currently the case with IOS, then virtually every kind of attack including double spend attacks is possible against the Bitcoin network either by the corporation(s) involved, by a government or as a result of malware in the “walled garden”. The key here is not the complete elimination of “walled gardens” but rather that they be prevented from having a majority market share.
It is therefore critical that in order for Bitcoin to be viable “walled garden” business models such as is the case with Apple's IOS must either fail or be at least prevented from reaching a majority market share.So what is the solution? In the case of iPhones it is very simple jail breaking. This, for smart phones, is now legal in the Unites States thanks to the efforts of the EFF among others. One simply needs to accept the fact that Bitcoin is fundamentally incompatible with IOS unless the IOS device is jail broken.
My suggestion to the OP here is very simple. Release the software under either the GPL v3 or the AGPL v3 so that it can be distributed for jail broken iPhones via the Cydia store
http://cydia.saurik.com/ for example. I am suggesting GPL v3 or AGPL v3 because of the strong anti Tivoization provisions in these licenses that will keep the software out of the Apple store and similar “walled gardens” such as the one planned by Microsoft. If Apple at a subsequent date changes its mind the OP can then, in addition to the GPL v3 or AGPL v3, license his software under a propriety license for distribution through the Apple store for a royalty. This has the added benefit to the Bitcoin network of providing a financial incentive to jailbreak iPhones by in effect “taxing” the walls of the “walled garden”.