Mr Bebbington, from Shrewsbury, was last seen entering the River Severn in the area around the Dana Steps in Shrewsbury at around 7.20pm on Tuesday. The 22-year-old has not been seen or heard from since.
Police have been joined in the search of the river by Shropshire Fire and Rescue, the National Police Air Service, Severn Area Rescue Association and underwater search teams.
Inspector Edward Hancox said: "We are keeping an open regarding Thomas's disappearance and whilst a lot of our focus has been on the river in the area where he went missing we have also been carrying out other enquiries in the surrounding area in the hope of locating him.
"He was not seen to exit the river, but we cannot rule this out."
Anyone with information should call 101 and quote incident 652s of November 10, 2015
Police divers were today continuing their search for Mr Bebbington. Paths near Sydney Avenue and Shrewsbury weir were taped off, which West Mercia Police confirmed was linked to the search.
But police say that they have so far found nothing in connection to his disappearance.
The alarm was raised at 7.20pm on Tuesday by a concerned passer-by saying a man had got into difficulties after trying to swim across the river close to the former Dana Prison.
The police helicopter was joined by boats and search teams late into the night.