So it appears to be an issue just of making b43 get loaded at boot (assuming that your wireless actually worked after you manually modprobe b43). You should be able to make the system auto-load b43 by adding it to /etc/modules:
echo b43 | sudo tee -a /etc/modules
If not, you could write a boot script to do it:
echo '#!/bin/bash' > /etc/init.d/
echo 'modprobe b43' >> /etc/init.d/
sudo chmod +x /etc/init.d/
sudo update-rc.d defaults
I also see that it's whining in dmesg about your having an out-of-date firmware file. If the card doesn't actually work even with b43 inserted, that could be the problem, but you should be able to download a more recent firmware file easily enough and copy it to /lib/firmware.