The 51-year-old writer, who created the Electra Brown series for teenagers, was last seen walking her dog near her home in Royston, Hertfordshire, on 11 April.
Despite extensive searches her body has not been found.
A man, 55, from Royston, arrested on suspicion of murder, disposing of a body and the theft of her money, has been bailed until August.
He was detained on Monday morning and questioned by detectives in Royston.
More on this and other news from Hertfordshire
Forensics teams searched the home she shared with her partner, Ian Stewart, and a holiday home the couple own in Broadstairs, Kent.
It is believed the Northumberland-born author left her Royston house to take her miniature dachshund for a walk
She had left a note saying she wanted some time on her own and was going to stay at their holiday home in Broadstairs.
Mr Stewart reported her missing four days later having travelled to Kent and established she had not been there.
Hertfordshire Police have found no trace of Ms Bailey and one month after she went missing, admitted "she seems to have simply disappeared".
Detectives said they are continuing to search her Royston home, but searches at the Broadstairs property had been completed.
As well as the teenage book series, the author wrote a blog called Planet Grief after her husband of 22 years drowned on holiday in Barbados in 2011.
A man arrested on suspicion of murdering missing children's author Helen Bailey has been released on bail.