Graeme Hicks was arrested by Essex Police officers who boarded a bus in Coggeshall Road, Braintree, shortly before 5.30pm on December 27.
The officers responded to reports of a man exposing himself and sexually assaulting passengers.
Hicks, of Old Chapel Drive, Stanway, was subsequently charged with sexual assault, indecent exposure, three counts of assault by beating of an emergency worker and possession of cannabis.
Detective Inspector Andy Drake said: “If you’ve been affected by this man’s behaviour, whether on a bus or elsewhere in the Colchester and Braintree area, please come forward and speak to us.
“If there have been other offences, we want to be able to build the strongest possible case against Graeme Hicks to ensure he is dealt with as robustly as possible by the courts.”
The 32-year-old has admitted each charge and will be sentenced at Chelmsford Crown Court on January 27.
DI Drake said: “As this investigation progressed quickly, it became increasingly possible that Hicks’ offending is not restricted to this incident on the bus on December 27 and I would really like to urge anyone who believes they have witnessed or been victim of Hicks’ concerning behaviour prior to this incident to please come forward and report it to us.
“We want to ensure that those people who exhibit this type of incredibly concerning behaviour are dealt with as robustly as possible when they are put in front of the courts.”
Any victim of Hicks, who has not contacted police, is urged to do citing the investigation reference 42/193622/24.