I don't think you can do that in a plain Managed network.
When you associate with your AP you associate with the MAC address of your desktop. When your desktop bridges a MacBook frame to the wlan0 interface, it has to spoof the source address. Even if wlan0 allowed the spoofed address to go through, your AP would reject that spoofed MAC because that MAC never associated with it.
You would probably need WDS support on both sides for it to work. That way you could send the frame with both MAC addresses. I have no idea if mac80211 supports that.
Ok thank you a lot for the explanations. I think I'll give up with the briding idea for now and will setup a classic router (standard or NAT, I am not sure).