If you have some other kind of Internet access on your computer, you can download the firmware by simply installing the b43-fwcutter package which does the download and setup for you automatically.
To install b43-fwcutter issue the following command in a terminal (under the desktop menu Applications > Accessories > Terminal) and follow the prompts:
~$ sudo apt-get install b43-fwcutter
Since Ubuntu 11.04 Natty Narwhal additional installation of the package firmware-b43-installer can be helpful and/or necessary, respectively:
~$ sudo apt-get install b43-fwcutter firmware-b43-installer
or, if you need a legacy driver, use:
~$ sudo apt-get install firmware-b43legacy-installer
Under the desktop menu System > Administration > Hardware/Additional Drivers, the b43 drivers can be activated for use.
Note: A computer restart may be required before using the wifi card. LiveCD/LiveUSB
For temporary use with the LiveCD and LiveUSB environments, instead of a computer restart, in a terminal issue the following commands:
~$ sudo modprobe -r b43 ssb ~$ sudo modprobe b43
Note: Allow several seconds for the network manager to scan for available networks before attempting a connection.
from WifiDocs/Driver/bcm43xx - Community Ubuntu Documentation