"Batgirl?" Thor became very quiet. He supposed her nickname would work well enough, not realizing she might be unwilling to give her proper birth name.
"I can take you somewhere safe to clean up," he offered. When she didn't turn down his gesture to lift her gently into his arms, Thor held her carefully in one, swung his hammer with the other, and they took off in flight. It was not as fast at Thor could have moved, but human bodies were fragile and the one he carried was always injured. The flight wasn't far but gave Batgirl a glimpse of The City from above.
They landed on the balcony of his penthouse. Thor set his hammer down on the balcony and used both arms to carry Batgirl into his home where he set her gently in a spacious washroom to clean up.
"When you are finished, we shall see about fetching your motorcycle."
Thor wondered if he should call Siggy. She might have knowledge of the healing arts in order to patch up Batgirl but it was late and he didn't wish to disturb the woman or the Peggy Carter that roomed with her.