I was using my e-mail address to login to the website and assumed I needed to use the same for logging in to the BAM through the BOINC client.
From the FAQ:
Please make sure you are logging in with your username and password, NOT your email address and password!
If you still can't log in, try to recover your password, find the text "Problem with login?" at the top of this page and click it.
If the password recovery claims that your username or email address can't be found or if you do not receive the recovery email then please make sure you really have an account at BOINCstats/BAM!. An entry in the stats tables is not the same as a BOINCstats/BAM! account, you need to create that separately!
You can find the username by going to BAM > Main account page
Use that user name to login from the BOINC client.
It's been a while since I've been here and used BOINC.