Hi Kenneth,
I'm a little surprised that your experiment with jury-rigging the bulb to the two bare wires didn't work; frankly the socket isn't exactly a technological marvel; it's just a way for those two connectors to touch the contacts on either side of the bulb. Since we're talking about an AC signal here it shouldn't matter which way the bulb is connected either, but I'm with you; I'd try it both ways just to be sure.
Anyway, assuming you can't get it to work with the bulb, then what you've got without that bulb is a series circuit with an open circuit where the missing bulb is. In order to complete the circuit, you have to reconnect the two sides of the circuit; you've got three wires there, two on one side and one on the other. Snipping off the connectors and twisting all three wires together with a wire nut should do the job.