Trundle's goal in the 29th minute provided Swansea with their seventh win of the campaign and they had enough chances to have won by a bigger margin.
Sam Ricketts and Adebayo Akinfenwa both struck the woodwork while Izzy Iriekpen missed an easy opening.
For Bournemouth, defeat provided the unwanted statistic of managing to score in only one of their last seven matches.
Without eight injured players, Bournemouth struggled to make an impact despite having plenty of possession.
James Hayter twice went close to adding to his four goals this season but he was denied each time by outstanding saves from Willy Gueret.
Gueret tipped over a 43rd minute shot from the lively Bournemouth striker and then dived to his right 11 minutes later to keep out a goal-bound header.
The goal which separated the sides came after a corner from the left by Kevin McLeod.
Iriekpen's close range shot was superbly blocked by Gareth Stewart but Trundle was unmarked when he ran in the rebound.
Swansea had Marcus Bean booked for a foul in the 39th minute as the visitors dominated the first session with only Trundle's goal to show for it.
McLeod shot over the bar from a good position and Stewart got down to hold a low left-foot shot from the speedy Trundle.
McLeod headed over the bar and Ricketts' shot hit the woodwork with the aid of a deflection.
Bournemouth improved after the break but even then Akinfenwa wasted two clear chances and drilled another shot against the underside of the bar after brushing off a challenge by Neil Young.
Swansea wasted the best chance of the match in the 64th minute when a shot from Roberto Martinez was fumbled by Stewart and somehow Iriekpen scuffed a shot wide from six yards when it looked easier to score from the rebound.