The two teams meet in an FA Trophy second qualifying round tie at Westleigh Park tomorrow (3pm).
Whatever happens, the two teams will meet again in Essex on Tuesday night – either in a Trophy replay or in the Ryman League premier division.
Bradbury admits playing the same opponents in such a short space of time is never easy.
His team have gone three games without a win in the league but came through a tricky tie at Cirencester Town in the last round.
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The Hawks have struggled to make the most of their chances in recent times so Bradbury is considering whether to change things up front.
Eighteen-year-old Alfie Rutherford started in the last Trophy game and made an impact by scoring the opening goal of the game.
He produced a cool, calm composed finish after being put clear of the home defenders by a clever Wes Fogden header.
Rutherford has a good chance of being given another Trophy start and has shown a knack of scoring goals whenever he has played this season.
Bradbury may decide to stick with his other starting striker at Cirencester, James Hayter.
He said: ‘James Hayter scored a hat-trick in our 4-0 closed-doors friendly against Bashley on Monday night.
‘We have not been scoring an abundance of goals recently.
‘In Alfie and James we have a couple of lads sitting on the sidelines who have showed they can score.
‘But it is not just down to the strikers to be scoring goals.
‘We need other players to chip in.’
In the closed-door friendly Bradbury included youngsters Marley Ridge and Alfy Whittingham, as well as Andreas Robinson.
They all did well and are in the frame to replace suspended captain Brian Stock, who will miss the first encounter with Billericay after picking up five yellow cards this term.
Theo Lewis would have been a natural successor but he is still out injured.
Bradbury reckons it could be another week to 10 days before he is ready to return.
The home side are boosted, however, by the return of central defender Ryan Woodford from a one-game suspension.
Fellow central defender Ed Harris looks as though he has recovered from his knock to the head suffered at Hendon.
Harris collided with team-mate Lee Molyneaux which left him with a bump the size of an egg on his forehead.
Billericay are the form team in the Ryman League premier division with just one defeat in the last 14 games.
Bradbury predicts the Hawks will need to show all their fighting qualities if they are to get through.
‘We must make the most of home advantage in the Trophy and then turn our attention to getting league points on Tuesday,’ said Bradbury.
Hawks: Young, Strugnell, Woodford, Molyneaux, Williams, Robinson, Fogden, Swallow, Rutherford, Hayter, Barker, Searle, Prior, Paterson, Harris