You might be able to so something with multi-site, but beyond my knowledge
I’d just install wordpress and my theme in the sub-domain and add the bbress plugin, and have maybe a coupe of menu items, eg forums and login
If you only want to have a forum on that site install WordPress and bbPress in the domain forums.example.com. If you want to have separate blog and forum you should look at WordPress Multisite using sub domains, your forums would be the 2nd site at forums.example.com and your WordPress blog would be at eaxample.com.
A good starting point is https://codex.wordpress.org/Create_A_Network
