Draco hadn't been certain whether anything would be necessary to help slow the bleeding until he had cleaned the blood and seen that it was still coming. Then he dug into his pocket for his handkerchief, embroidered with his family's crest, and offered it to her. Getting blood out of it wouldn't be difficult, so he hardly minded.
"Je serai de retour dans un instant," he said, and moved to get the potion from the hallway bathroom, as she'd indicated. He returned with it in his hand, and offered it to her.