The body of Bei Carter, 49, was discovered by police at the Morayland Hotel, Marshall Avenue, late on Friday.
Detectives from Humberside Police have said they want to speak to John Heald, 53, in connection with the murder and warned the public he is “dangerous” and to call 999 if they see him.
Officers say they “strongly suspect” he is back in his native South Yorkshire and yesterday said there had been reported sightings of him in both Rotherham and Mexborough.
Yesterday South Yorkshire Police said they also wanted to speak to him in connection with a serious offence that took place in Sheffield on Sunday, July 13. Officers did not reveal any further details.
Det Supt Mathew Hutchinson, leading the search for the wanted man for Humberside Police, said: “There have now been reported sightings of John Heald in Rotherham and Mexborough and we have officers on the ground here to locate him.
“John Heald is a dangerous man and he needs to be found and arrested as a matter of urgency. He is wanted for a serious offence in the Sheffield area as well as for the murder of Bei Carter in Bridlington and I believe that people here in this local area know him and may well know where he is.”
Mr Hutchinson urged anyone who has seen him to get in touch.
“To anyone who might be helping Heald evade the police, I would say; consider your actions, this is a very dangerous man, he needs arresting before he can harm anybody else.
“I believe Heald poses a threat to the general public and therefore people should not approach him. If they do see him they should ring 999 immediately.”
Anyone with information can also contact the Major Incident Team on 01377 208989.
Officers say they believe Heald was a resident at the Morayland Hotel in Marshall Avenue in Bridlington when Mrs Carter was murdered.
They believe he may have approached friends to offer him shelter or say he may be sleeping rough.
Police said Heald, from the Rotherham area, could be looking for accommodation and it was important any hoteliers who are approached by him for a room contacted police straight away.
Officers placed a cordon outside the guest house after Mrs Carter’s body was found and crime scene investigators were at the address carrying out detailed forensic work.
South Yorkshire Police’s District Commander, Chief Supt Jason Harwin, said: “We are working closely with our colleagues in Humberside Police to quickly locate and arrest this individual.
“Additional officers are being deployed to support the investigation and to provide reassurance.”