Microchip has a great app note on using a PIC to send and receive X10 over power lines. It is here...
http://ww1.microchip.com/downloads/en/AppNotes/00236B.pdf
Since you only want to send a single bit, you could just steal some of the ideas and simplify.
Here is their block diagram for injecting a signal onto the mains...
You could use a PIC or an AVR (like and arduino) to generate the carrier as shown, or if you want to keep it simple you could use something like a 555 or even an RC oscillator, but keep in mind that an MCU like an ATTINY only costs like $1 today and will give you a more accurate and stable frequency base (especially if driven by an Xtal), and opens up possibilities for sending more than one bit (like sending error correction with the bit to make detection more accurate).
Here is their block diagram for a detector...
...which again uses a Microchip PIC, but that could easily be replaced with an AVR or even just a relay.
I'd really urge you to read the whole app note as there is a great explanation of how the carrier interacts with the mains, when you should send it, and even how to power your circuit from the same connection to the mains using a transformer-less supply.