Dominic Poleon had opened the scoring early on but after Jonathan Edwards was dismissed, Bostwick fired in to secure the short-handed visitors a point.
Oldham began the game on the front foot and Poleon struck in the ninth minute. A searching right-wing cross from Brian Wilson saw him peel off his marker to deliver an accurate header which went in off the far post.
Peterborough went close with a pair of drives narrowly off-target from Joe Newell.
Bostwick hit a powerful shot from 30 yards which was parried into the air by Oldham goalkeeper Joel Coleman, with Ricardo Santos unable to head the rebound on target under pressure with the goal gaping.
Oldham centre-back James Wilson struck a volley from outside the box which Ben Alnwick caught, before Edwards received his marching orders for a late hack on the Oldham player in the 67th minute.
Bostwick levelled after 76 minute when Newell’s corner was punched by Coleman straight to the midfield man, who finished powerfully.