Wireless headphones on a MacBook running 10.4 — Does Bluetooth work? Can MacBooks (10.4) stream music to Bluetooth headphones? If not, is my only other option to purchase bulky/expensive wireless headphones, or is there another way?
The Bluetooth profile necessary for stereo audio, A2DP, is supported by OS X since version 10.5 (aka “Leopard”). As you use 10.4 (aka “Tiger”), the answer to the first part of your question is:

Bluetooth audio only works in 64 kbit/s mono quality via the headset profile in 10.4.

Probably not what you want for music listening, even if the headphones support it. As to the second part of your question:

You are stuck with wireless solutions working via the audio jack, USB or FireWire.

In the case of USB / FW solutions (if such wireless solutions exist), check these for 10.4 compatibility before you invest.