Since my last update, I've learned a lot more about Bluetooth (for another project) and decided to give it a try for this project instead of AirPlay. I saw this project on Hackaday and bought the same adapter from Amazon on sale for $7.50. I also bought an audio amplifier for $6.78, also from Amazon.
I'm planning to remove the enclosure from the Bluetooth receiver so I can solder directly to it. I'll hook up the +5V and ground from the Bluetooth receiver to the audio amp, as well as the left and right audio channels. Then it's a simple matter of hooking the speaker up to the right audio channel (since I only have a single speaker) and plugging it all into the USB battery pack.
Also, the audio amplifier has a built-in potentiometer that controls the volume, so I might mount it onto the speaker enclosure.