The former Havant boss replaced Mark McGhee at Priory Lane earlier this month.
He has begun work by re-signing some fans’ favourites - with new arrivals expected soon.
Midfielder Sergio Torres has agreed to play for the National League South club for another year.
That news came after the big announcement that talent striker Charlie Walker has committed to another contract at the south coast side.
Midfielder Mike West will be back too, and fans will be delighted to see talented teenager Daniel Blackmore also put pen to paper.
More is expected of the Sports next season after a year which won’t live long in the memory.
Eastbourne finished the campaign just three points above the relegation places.
Bradbury, who won with division with the Hawks in 2018, is hoping for another season at the right end of the table.