You can integrate WordPress with Discourse by having your WordPress site function as the Single SIgn On provider for Discourse. Single Sign On (SSO) can be configured with our WordPress plugin.
When SSO is used between WordPress and Discourse, usernames, user full names, and email addresses will be synced between the two systems. It is also possible to pass some additional information in the SSO parameters. For example, the user’s bio could be sent to WordPress. If you want more integration than that between the two systems, it may be possible to do, but you might need to hire a developer to do the work for you.
I am not sure how BuddyPress stores user information on WordPress, but I would expect any user details that are added by BuddyPress to be available as WordPress user metadata.