The teams had been two divisions apart last season but Rotherham more than matched their high-flying visitors and were worthy of the point after forcing Cherries goalkeeper Asmir Begovic into a host of saves in an entertaining encounter.
Matt Crooks had an early shot diverted away from goal by the alert Chris Mepham but Bournemouth's first effort was closer when Junior Stanislas picked out Dominic Solanke - but he could not find the target as he slid in ahead of goalkeeper Jamal Blackman.
Blackman was then at fault as he collided with Solanke on the left-hand side of the box to give away a penalty. Stanislas took his time from the spot before striking it down the middle to give the visitors a 20th-minute lead.
The hosts were almost level inside a minute with Joe Mattock crossing for Jamie Lindsay - but his diving header was tipped over the top smartly by Begovic.
It was from the left flank where Rotherham got level on 37 minutes with Ladapo slotting into the bottom corner clinically after being found by Mattock.
Stanislas came close to his second either side of the break. He first tried to catch out Blackman at the near post with a long-range free-kick and was then denied by a diving save from the Chelsea loanee.
But it was the home side and Ladapo celebrating a double five minutes into the second half as the striker beat Begovic with an audacious chip into the far corner from the left side of the box.
The goal came just moments after Begovic had denied Lindsay's stinging drive from the edge of the box.
The Cherries levelled on 63 minutes, with substitute Diego Rico having an instant impact and teeing up Solanke to head home from 10 yards out.
Begovic again came to the rescue to keep out Angus MacDonald's stunning acrobatic volley with a diving save. Crooks turned in the rebound but was ruled to be offside.
Blackman beat Solanke to a through-ball as their own personal battle continued and Philip Billing smashed over from the edge of the box as the visitors cranked up some late pressure.
Jefferson Lerma momentarily had Blackman scrambling but his long-range chip, with the goalkeeper way off his line, was just over the bar as Jason Tindall and his team had to settle for a point.