Both sides were docked 17 points at the start of the season following spells in administration and were eager to take the points to edge away from the drop zone.
Midfielder Danny Hollands rattled the post after 11 minutes after poor defending by the Millers.
Rotherham's best chance fell to Marc Joseph but his close-range volley was palmed away by Shwan Jalal.
Bournemouth's Darren Anderton thought he had wrapped up the points late on but his stunning 20-yard strike rebounded off the inside of the post.
Rotherham stay 22nd, two points behind Grimsby, while Bournemouth are one place back on minus seven points.