Is it possible to have a bidirectional arduino connection with one wire?

Is it possible to have a bidirectional Arduino connection with one wire; in a single-master multi-slave configuration ? Assuming all of them share the same 5V and ground lines.

Yes. It would be very similar to developing a wireless protocol, where all the devices use the same channel/frequency. The start/stop indicator would be more complicated, as you would have to have addressing or signaling to indicate which device is to receive the data being sent, or to indicate to a device when to send back data.

As well as the 1 wire bus you can also have half duplex connections like the RS485 Only with out the differential drive but using tri-state outputs and a protocol to effect direction switching.