Nope, last time I loked into forums was years ago, and I decided to write my own 😃. Can't really recommend that though. It does however give you a nice practice, and will allow you full integration with the rest of the site.
That being said.. When you acquired the skills to write a reasonable BB, you can probably easily hack into existing BB as well to integrate.
Just note: Many blackboard run the risk of being hacked at some time, as so many people use them. I know that e.g., PHPbb had a version which was so open to fake users that in the official forums people were recommended to modify the signup procedures. You would do that anyway though if you want to integrate your logins for tha tBB and the site.
All in all it is not very complex. It is a matter of finding the user registration & login routines and re-using them in your site. It is a lot of work in my experience.