To actually make it work, you would need to preformat your data very specifically, and the data you want to allow to be processed would need a subkey to unlock the parts you want processed.
I don't see a way to make it a open standard. The processing steps would need to be part of the key.
Anyway If someone figured it out I would be very interested to be sure they weren't just trying to slap a it's encrypted to meet some standards required. And..also, what amount of data processing does Alice need to do that required outsourcing to Bobs machines. Data processing and anaysis is cheap.
The point is to not have subkeys or any other way to access any part of the plaintex - as the goal is generally to offset the computation and the costs of it to another party. And yes, most likely it will require a very particular format of the data, and in all likelihood will allow only for a limited set of operations.