The problem with just straight sending the bits is that with an IR receiver, it has to receive a signal at a specific frequency, eg the IR receiver only outputs that a signal is detected when the IR LED is blinking (I tried with always on and it didn't work, then I tried blinking it at some arbitrary frequency and it worked sort-of). The SoftwareSerial you provided is actually the first thing I tried to do, before I realized I needed to have an actual frequency along with the data.
I'm thinking that I can blink the LED at the frequency (in order for the receiver to detect it) when I need to transfer a 1 and turn it off when I need to transfer a 0, but I don't know how to easily sync up the sending and receiving to make sure it goes over well.
Here is the spec of an IR receiver: http://www.vishay.com/docs/82090/tsop48xx.pdf
. Look in the section of "TYPICAL CHARACTERISTICS", where it shows that for the receiver to detect the IR light, the light has to be turning on and off.