Spireites midfielder Gary Liddle was sent off after only 16 minutes for a foul on Kane Vincent-Young.
Chesterfield kept the U's out until Drew Wright broke free with 20 minutes remaining, cutting the ball back for Bonne to strike right-footed.
However, three minutes later Lee Novak converted from the spot after he was felled by Richard Brindley.
Colchester's winless run in League One stretched to 17 matches as they remain rooted to the foot of the table while a point was enough to take Chesterfield out of the relegation places.
Macauley Bonne scored his first goal in 11 games but Colchester were held to a draw by 10-man Chesterfield.