Jason Prior’s 74th-minute penalty earned a deserved point for the Rocks in a rather disjointed mid-table Ryman premier battle at an icy Nyewood Lane.
The Rocks were unchanged from the win at VCD, with striker Prior having recovered from a leg injury that forced him off early in that game.
There was an early scare for Bognor when a quick Billericay free-kick almost played Rowan Liburd in on goal but Chris Winterton was quickly out to gather.
The visitors needed a defender to clear off the goal-line in the fourth minute as Doug Tuck shot goalwards when keeper Joe Wright failed to gather a corner.
Jake Thomson had only himself to blame when picking up a seventh-minute booking. He lost possession just inside the Billericay half and had to pull back his opposite number to stop him getting away.
Winterton started a flowing move with a clever drop-kick out to Parsons on the right. After two one-twos the winger had sight of goal but dragged his shot well wide. Then a Parsons cross was spilled by Wright under pressure from one of his defenders but he grabbed the ball before it could roll over the line.
For the Essex side, Harry Baker’s cross from the byline caused panic in the Rocks defence but they scrambled it clear, and play was held up for treatment to Liburd, who’d suffered a head injury.
Bognor won their first corner on 16 minutes through good work by Ollie Pearce.
Liburd was unable to continue after his injury and was replaced by Liam Nash.
Harvey Whyte’s run and pass from the right-back position set up Tuck for a shot at goal. It wasn’t bad but it drifted wide without troubling Wright.
Parsons was Bognor’s liveliest player and another cross from the right, after he went past his full-back, almost presented Pearce and then Stuart Green with a chance.
Parsons took a long pass beautifully and sent in another cross, a low one this time, but Pearce was beaten to by a defender and the danger was cleared.
There was drama of an unusual nature just after the half-hour when ref Paul Saunders pulled up with a hamstring injury. He hobbled off and the players came off too as Rocks officials waited for a new qualified linesman to get ready and allow a reshuffle of the officials’ team.
When play resumed after an 11-minute hold-up, Green played Parsons in inside the box but he fluffed the shot and it flew wide.
Glenn Poole threatened for Billericay with a left-footed drive after a one-two just outside the box, but it was too high.
Billiericay gifted Bognor a 40th-minute corner and when it was cleared, Tuck hit a terrific volley that was headed off the line by Teddy Nesbitt.
Billericay right-back Ola Williams was booked after the half-time whistle was blown - for reasons which were not immediately obvious.
Parsons wasted a golden opportunity to open the scoring three minutes into the second half. Played into space on the right, he was caught between crossing and shooting and blasted the ball across goal and out for a goal-kick.
Bognor looked the sharper side at the beginning of this half but were still lacking a cutting edge where it mattered. That was shown when Pearce ran free down the left but found a defender with his low ball into the box.
Prior was poised to head in a Parsons cross on 59 minutes but Ryan Scott headed it behind for a corner which was cleared. Then Prior did meet a Parsons cross but glanced a header just wide when he would have expected to score.
Typically, after all the Bognor chances, Billericay took the lead on 62 minutes when Ricky Sappleton timed his jump perfectly to head a cross from the left beyond Winterton and in off the stanchion.
Sappleton tested Winterton again five minutes later but the keeper held his fiercely-hit shot.
The goal seemed to have knocked Bognor out of their stride a little and had lifted the visitors.
Charlie Oatway replaced Thomson with 22 minutes left, while Ryan Melaugh replace Baker for Billericay.
Green found himself with a chance to shoot from 20 yards on 72 minutes but could only bend a weak shot straight at Wright.
But the Rocks did draw level two minutes later when Pearce was sent sprawling as he ran on to a through-ball in the box. After keeper Wright was booked for protesting, Prior confidently sent him the wrong way from the spot.
The referee was on the verge of losing control once or twice, and Billericay boss Craig Edwards earned himself a talking-to for questioning numerous decisions. Edwards and his staff also had a major difference of opinion with a couple of fans standing near the technical areas.
A corner for Bognor as the game entered its final ten minutes led to a couple of half chances for Prior but one was blocked, the other saved by Wright.
Billericay should have been back in the lead with seven minutes to go. Sub Nash seemed certain to score with the ball at his feet yards from goal but Whyte heroically blocked it on the line. Soon after, Poole sent a low shot well wide.
Bognor almost snatched a winner when Green’s driven cross from the right was deflected on to a post by a defender.
A 90th-minute free kick held promise as the hosts went for the win but when it fell to Green, he screwed his shot across the six-yard box and out for a throw. That was the final chance and a point apiece left the two teams still 11th and 12th in the table.
Bognor go to Kingstonian on Monday, when striker Terry Dodd is likely to be in the squad.
Bognor: Winterton, Whyte, Crane, Tuck, Woodford, Robson, Green, Thomson, Prior, Pearce, Parsons. Subs: Oatway, Sackman, Lawson.
Billericay: Wright, Williams, Nesbitt, Edwards, Halle, Scott, Baker, Poole, Sappleton, Liburd, Dunne. Subs: Akosa, Obafemi, Melaugh, Nash, Lumley.
Ref: Paul Saunders (Hove)
Report by Steve Bone