The timeline for developing reliable liberty responses varies enormously based on the horse's training history and personality, the trainer's experience and clarity of communication, the frequency of sessions, and the definition of reliable. A horse that will follow the trainer around a round pen at liberty is a very different standard from one that performs lateral work and complex sequences at liberty in a large arena.
Basic send and draw in a round pen can often be established in a single session with an already well-handled horse that has a solid groundwork foundation, simply by removing the halter in a familiar environment and transferring existing cues to body language alone. But the depth and reliability of that communication — the kind that holds up when the horse is fresh, in a new environment, or distracted — takes months of consistent practice to develop.
For truly advanced liberty work — performing collected movements, working in large open spaces, working with multiple horses — the development timeline is measured in years. Horses that demonstrate spectacular liberty performances in online videos have typically been in training for many years, and the relationship underlying those performances has been built through thousands of hours of daily interaction.