Something comforting to focus upon, something pleasant, something that would give her strength and security. From his new memories of how Bill used her mother to fight back against the Monk's power, the Doctor knew how significant this woman was to Bill's life, even though she was for the most part a figment of Bill's imagination.
When he noticed that Bill was falling asleep, the Doctor was content. The TARDIS would continue to monitor her to make sure she'd be alright, while at the same time mending her injuries. The Doctor briefly touched Bill's hand with his fingertips, a reassuring gesture for for himself than her, then muttered softly, "You'll be alright. I'll take care of you." Then he turned to leave.