That’s how it works, the bridge makes it possible to post your content to both. And if people who interact with it also use the bridge, it will be visible on both as well. The only downside is that you can’t interact with people who don’t use the bridge and at the same time are not reacting to your post on the same platform you are. For example, I have Mastodon account and use the bridge, if someone who only uses Bluesky, but not the bridge, comments a post by me, I have no way to react.
That’ll show them!