Officers said the attack on Friday, March 6, was not racially motivated and are urging people not to protect family members who they suspect might be involved.
West Yorkshire Police were called to the scene at Beeston Road, near to Malvern Road, at 10.50pm on Friday, where they found the woman suffering from a head injury.
She was taken to hospital where they also found she had serious hip injuries.
Detective chief inspector Elizabeth Belton, of Protective Services (Crime), said: “This has shocked the local community.
“I want to put an end to unhelpful speculation that this was a racially motivated attack.
“The victim was Asian, as is the person we want to speak in connection with the incident.”
Det Chief Insp Belton added: “We think the man has been in the area for some time before the incident and may have attracted attention.
“I would appeal to anyone who saw a man with blood on his shirt in the area that night. I would encourage people to think – was there something out of place – or did someone come home with blood on their shirt?
“This is no time for family loyalty – this was an horrific incident and the victim is lucky to be alive.”
Potential witnesses including a woman who was standing at the bus stop shortly before the attack and got on board the number 1 or number 74 bus, and a man who was seen running nearby, are being urged to come forward.
The suspect is described as a slim, Asian man in his early 20s with receding dark hair.
Call police on 101 or Crimestoppers anonymously on 0800 555 111.