By default, bbPress is set to automatically take links and turn them into embedded content.
When you post YouTube link in the topic or reply, when displayed, bbPress will embed the actual video instead of the link. To change this behavior, and show only the actual link, open WordPress Settings -> Forums (or bbPress) -> Forum Features, and find option for Auto-embed links, and disable it.
This will disable auto embed for all supported websites (Facebook, Vimeo, Twitter…).