If you like an independent bio plugin better, use it. Continue to use it even with bbPress. I can relate to the desire to limit plugins, but if the plugin provides important useful functionality, it’s worth making an exception to the no plugins rule.

You could also build your own bio box plugin, which could also contain any other custom code you develop. A single custom code plugin can replace any number of other plugins without incurring much of the overhead that’s often part of many plugins. Of course, some things are not worth custom coding because an existing plugin does something really well.