I'm quite sure it is Renai Kaidan Sayoko-san.
Synopsis from mangaupdates (emphasis mine):
Sayoko is an incredibly kind, but solitary, young kimono-clad lady who has certain supernatural abilities. She can see ghosts, and she frees them from their places of death by agreeing to let them haunt her instead. As a result, everywhere she goes, she is followed by an army of well-meaning spirits that only she can see. Her weirdness tends to throw any normal people who would have otherwise possibly become her friends.
Inaba is a poor college student who happens to accidentally run over Sayoko with his bicycle.
Sayoko normally is unable to interact with people for long periods of time, because since she is haunted she endangers the health of other people just by being close to them... But for some reason Inaba is completely fine with being around Sayoko even for long periods of time...
.... Just what's going on?
The scene where Inaba runs over Sayoko with his bicycle happens right at the beginning of chapter 1. Sayoko was bleeding from her head, but she was more worried about the boy's well-being than herself.
Also from chapter 1, Sayoko asked Inaba to lead her to the cursed shop where Inaba was supposed to work at but the manager ran away without paying his wages. When she arrived, she had a talk with the panda mascot, who died from a heatstroke. The panda mascot loved the smell of the restaurant, so he stayed and tried to advertise the shop, but every new shop opened there shut down in the end. She let the panda mascot possess her near the end of chapter 1.
The scene where the ghosts (not really demons, they are well-meaning ghosts) teased her about seeing the boy naked is from chapter 2.