How to upgrade bbPress? Read the official documentation on upgrading bbPress to be risk-free.
Here is the shortcut I follow which works fine:
1. Download the latest bbPress release and unzip it.
2. Upload the contents of the unzipped folder to your forum folder in the webserver. A BIG WARNING: Don’t upload the whole folder as such to replace the forum folder in webserver. Just upload the contents and add to the files in the forum folder in web server.
Visit your forum URL and follow the instructions.