I had some time this week to play around with Geiger Bot, and I have it at least mostly working with my Geiger Counter kit.
The circuit is shown (sorry for the poor quality photo).
I had trouble getting Geiger Bot to consistently register counts, so I went into the settings and selected custom GM tube, then selected I/o Settings -> Auto Adjust OFF. Then I adjusted the Volume Threshold to around 5000. You can also enable "Ultrafast rates", this seems to make Geiger Bot more sensitive to the pulses from the kit. If you do this, you can increase the volume threshold to 10,000 or higher.
The easiest place to get an iPhone headphone connector is probably by buying a cheap pair of headphones ($4 at Fry's) and cutting off the cord just below where it splits to go to the microphone and earbuds. Then carefully separate the wires and tin each one. Use a DMM to determine which wire goes to which position on the connector.