Accessing Team Folders in Bluebeam App

There are technically two different questions here, so I'll address them individually:

It sounds like the app you're referring to is "user-linked", that is, each user that wants to use it needs to authorize it to connect to their own account. (As opposed to being "team-linked", which would mean that a team admin could connect it to the entire team at once.) "User-linked" apps only get listed under each user's Connected Apps list, not the team's apps list on the Business Admin Console. (And in either case, connecting an app is initiated from the third party app itself, not from the app list in Dropbox.)

It sounds like your team is using the "team space" configuration, but the app you're referring to isn't allowing you to use the team space, only your member folder. The Dropbox API itself (which is the way that third party apps integrate with Dropbox) does offer the ability to operate in the team space, but the third party app will need to be explicitly written to support it. You may wish to contact the developer of the third party app to request that they update the app to do so.