The reason why Klaus didn't play the Star Monarch card when he first laid eyes on the bird was that he felt no resonance between him and the bird.
That was because the one they had fought for the past two hours was merely a clone. So he sensed no likeness between them. However, when she revealed her aura through the void, Klaus sensed it.
Of course, he could have stopped then, but he had to prove himself, and so he used the time and gravity law to push her to a corner.
Once that was achieved, he knew he had to stop before he angered the bird lady any further. Already, she had them on thin ice. If it were only Klaus and perhaps Rory, escaping would have been simple. But carrying the others along with him would have been impossible.
From his calculations, the time it would take to send them inside the Demon Bead before making a run for it would be four seconds. That was plenty of time for the bird lady to kill them all.
So he made a gamble, and it paid off.
