Yes. Bookmarks have been private since Twitter launched them in 2018, and they stayed private through the rename to X. No app or website can look up someone else's bookmarks, because X doesn't offer a way to do it. X's Help Center page About Bookmarks says: "No, Bookmarks are private and are only viewable to you within your X account."
That makes a bookmark the quietest way to save a post. A like is visible to the post's author, and a repost puts the post on your profile. A bookmark does neither.