The drapes!

This mysterious woman obviously has a lot of information pertaining to the matter in the woods. This incident is how you intend to prove yourself to your kingdom, there's no way in hell you're letting her get away.

You know she's faster than you, attempting to get to your feet and rush her would be a fool's errand. Looking around your chamber, you don't see much of anything that would be a help. Then, it dawns on you. While you were deligating boring matters of business for the kingdom, your servant, Sarah, followed your instructions, and currently hanging over the mystery woman are heavy, dense, decadent, dark-maroon drapes. Although you haven't utilized them to block out the sunlight from your chambers yet, you know it is standard for the heavy drapes in other chambers of the castle to be managed by a series of pulleys and counterweights... A quick glance around the chamber confirms this, and as luck would have it, you've been knocked right next to the main counterweight. Without a moment's hesitation, you swing your sword with all your might against the rope attached to the hefty counterweight.

The mysterious woman is too distracted priming herself to jump from the window to notice as the series of pulleys and ropes unfurl from their calculated positionings. The heavy drapes fall straight down onto the assailant, catching her off guard and envelloping her in a temporary velvety prison.

You quickly get to your feet, bringing your sword with you. Your robe has become unfurled in all the chaos, and you abandon the less-than-combat-ready garment on the floor. The heavy drapes on the floor next to the window frantically flail about. After a brief pause, you see an object abruptly tear through. You decide now is the time to jump into action, before she has a chance to use the dagger she was apparently concealing.

"Guards!" You shout through the door, "I am fine. Prime the catapaults, we have a flying intruder around the castle..." You're cut off by a muffled shout from underneath the drapes. You keep your sword primed and ready, pointed at the mass of fabric struggling on the floor. Finally, the torso of the intruder bursts forth from the now-ruined drapes, a look of fury on her face. "LEAVE HIM ALONE!"

Her moment of panic subsided, the woman looks down and sees you have your sword pointed directly at her. You say quietly to her, "I'll rescind my command, but you need to cooperate with me. Understand?" She sits quietly for several seconds, either trying to comprehend what you said, or contemplating what other options she has. She finally gives in, nodding her head. "Guards," you speak again at a raised volume so they can hear you through the door, your sword and gaze never leaving focused position on the intruder, "Everything is fine. I'm afraid I must have knocked some items over in a confused state coming out of a bad dream. Please disregard my previous orders and return to your posts." You hear a gruff, annoyed voice say "Yes, your majesty" and walk away. "Now, I'd suggest you disband that dragon of yours and get comfortable so we can discuss matters."

You can only barely see the woman's face, the cloak and scarf still covering the majority of it, but her body language show she feels moderately defeated. She pulls the scarf down from her mouth and issues a series of 3 shrill, short whistles. You look out the window and think you make out a shadowy, dragon-like figure glancing over its shoulder as it flies away.

Up until this point you thought your sleep-deprived eyes were just playing tricks on you, but after a second sighting, and this woman complying with your half-crazy demands, you can't believe it! A dragon! There were legends of dragons, certainly, but you never thought they actually existed... You even considered them last night whilst researching, but brushed them off as a real possibility. You take a moment to regain your composure, you still aren't sure if this woman is armed or dangerous. " Now, I need you to relinquish any weaponry you may have. As you said, I mean no harm as well."