Just 18 percent of Germans were against tougher video surveillance, according to the survey by Infratest dimap, released by broadcaster ARD.
Last Monday, a blue sports bag left on a platform in Bonn's main station was found to contain an improvised explosive device. The detonation device was reportedly triggered but did not go off.
Prosecutors believe Islamist extremists were behind the botched attempt.
The train platform was not under full surveillance, and despite the presence of video cameras, no footage of the bag drop-off was recorded.
The only images available of the suspects themselves were taken at a nearby McDonald's restaurant.
The case has ignited a fierce debate among German policy-makers - with politicians from Chancellor Angela Merkel's conservatives, the Christian Democratic Union, calling for more video surveillance.
The centre-left Social Democrats, as well as the Greens and the Left Party, oppose the CDU stance.
Earlier this week, Green Party parliamentary leader Renate Künast told the Süddeutsche Zeitung that Interior Minister Hans-Peter Friedrich should instead push for better cooperation between the various offices and targeted efforts to prevent future attacks.
"We need effective security authorities, not blanket surveillance," she said.