Knowing victory would put them top of League 2, Dale still had chances of their own but will be pleased with a point after keeper Josh Lillis made a stunning save at the death.
The visitors suffered a blow as top scorer Scott Hogan, named League 2's player of the month earlier in the day, was forced off through injury, but Dale almost caught Bury napping as Allen headed over from Peter Vincenti's cross.
The Shakers replied with Danny Nardiello firing over and moments before the break, Henderson was sent off after pulling back Jake Carroll.
The hosts almost broke the deadlock just after the restart as Pablo Mills sliced a close-range effort against the bar, yet Dale hit back as Michael Rose and Peter Cavanagh fired inches wide.
Bury substitute Tom Soares then had a close-range effort saved by Lillis while Brian Jensen parried a 20-yard shot by Dale sub George Porter.
But Dale were indebted to Lillis as he denied Nardiello before tipping over Carroll's last-gasp header.
- Sports & Recreation
- Ian Henderson
- Josh Lillis