CB radios use a variety of connectors, the most common being the 4 and 5 pin DIN types, with 4 pin Cobra/Uniden style being the very most common(what you would likely find at a truck stop). You can verify which pinout your radio uses by checking the pins on the the CB socket with the microphone unplugged, noting which pin has continuity with the ground of the CB.
Once you have identified your pinout, you should simply be able to build an adapter cable(connectors are widely available) that splits the MIC signal and the ground out to another connector. Since you are designing your own circuit, you shouldn't need to add any circuitry to your adapter since you could design your circuit with a high-enough input impedance to be able to rely on the termination of the MIC signal in the radio.
Walcottradio.com has an excellent illustration of the various pinouts("Mod"="Microphone"):

Yours is likely the top-left most pinout in the chart...