IPhone : iOS Transfer sizeable data via BLE

I'm trying to send a bit of data (32KB) between two iPhones (6+ and 4S). I understand BLE is not intended for large data transfers, but I'm certain there should be a way around my problem.

I have a characteristic setup as follows:

[[CBMutableCharacteristic alloc] initWithType:[CBUUID UUIDWithString:someID]
                                   properties:CBCharacteristicPropertyNotify
                                        value:nil
                                  permissions:CBAttributePermissionsReadable];

To send it, I break it down into chunks and send it like this:

[self.peripheralManager updateValue:chunkOfData
                  forCharacteristic:myCharacteristic
               onSubscribedCentrals:aSubscribedCentral];

However I noticed that it takes a good 20 sec. to get the data through which doesn't really work for me... My question is: how can I achieve a reasonable speed?