Jobi McAnuff came closest for the O’s early in the first-half when his free-kick rebounded back off the bar but the O’s found it difficult to test the Aldershot keeper throughout the game.
Justin Edinburgh named an unchanged squad from the side that took three points from Wrexham AFC.
Orient began the game on the front foot and enjoyed large spells of possession inside the Aldershot half.
The O’s first chance on goal came after a quarter of an hour, Josh Koroma was brought down on the edge of the box by Dominic Bernard who was handed a yellow for the foul.
Jobi McAnuff stepped up to take the resulting free-kick but struck his effort against the crossbar before Aldershot managed to clear the danger from the loose ball.
The O’s attacked well down the right and McAnuff linked up well with Craig Clay before the former’s driven cross was cut just short of finding Bonne’s run into the box.
Minutes later, Dale Gorman broke in to the area from the left wing, his initial cross was clawed clear by Will Mannion in the Aldershot net, before the ball fell to the Irishman again, this time his shot on goal was cleared off the line.
Aldershot saw a rare chance on goal come from distance when Matt McClure struck inches high from 30-yards.
Aldershot were forced in to their second change of the game after just 30 minutes of play as McClure hurt his shoulder prior to his effort on goal, the forward was replaced by Josh Barrett.
The first change came 15 minutes earlier when Adam May was forced off and replaced by Shamir Fenelon.
Four minutes before half-time, Bonne flicked McAnuff’s clearance in to the path of Koroma who ran through on-goal but was challenged by Kinsella as he set up the shot. The tackle from the Aldershot defender was enough to force the ball away from immediate danger.
Koroma was involved again during injury time when his quick shot from the right almost caught out Mannion as most in the box expected a cross.
Edinburgh made one change at the break, Saturday’s goalscorer James Brophy replaced Craig Clay. McAnuff moved in to Clay’s position to accommodate Brophy in his natural position of left wing.
Orient started the second half in similar fashion to the first, Dale Gorman’s initial shot was deflected wide of the post before Josh Coulson hit over from the resulting corner.
It was a lively start from the home side and after Dayton was fouled on the right side, Joe Widdowson rose highest but headed McAnuff’s free-kick just over the target.
McDonnell’s free-kick from the left forced Dean Brill to palm the dangerously whipped set-piece over his bar.
Orient pressure almost paid off after 55 minutes when Dayton cleverly found Gorman’s late run into the box, however the midfielders low shot was excellently kept out by Mannion.
Ten minutes later, Myles Judd’s deep cross dropped to James Brophy at the back post but the ball didn’t fall in time for the winger to get his shot on target.
The game evened out midway through the half, but James Alabi won the ball and headed it down for Bonne to strike, however the forward’s first time effort was sliced wide of the target.
The front pair linked up well again a minute later, Bonne’s flick found the run of Alabi whose left footed strike was well save by Mannion in the Aldershot net after the forward ran through one-on-one.
Aldershot almost snatched an opener in the 83rd minute, Berkeley-Agypong’s cross found the head of a free Adam McDonnell in the centre of the box but Joe Widdowson was in the right place at the right time to block the attempt.
Just as the referee announced four additional minutes, Marvin Ekpiteta headed wide of the target from McAnuff’s corner.
Orient continued to apply pressure to the visiotrs but their defence stood strong as the points were shared in E10.
The O’s are back at home again this Saturday 1 December against Gateshead. Tickets for this Vanarama National League game at The Breyer Group Stadium are available now at www.onlyoneorient.com.
ORIENT: Brill, Judd, Ekpiteta, Coulson, Widdowson, McAnuff, Clay (Brophy 45), Gorman, Dayton (Alabi 65), Koroma, Bonne
SUBS: Janata, Happe, Harrold
BOOKED: Clay (35)
SHOTS: Mannion, Kinsella, McDonnell, Howell, Bernard, Gallagher (C), McCoy, May (Fenelon 14), Osho, Grant (Berkeley-Agyepong 68) McClure (Barrett 30)
SUBS: Cole, Wanadi
BOOKED: Bernard (15), Kinsella (35), Barrett (73)
REFEREE: Christopher Pollard
ATTENDANCE: 4,289 (274)