About 1.4 million free journeys took place in the first trial year of the scheme, costing Weca £1.4m.
Research from the University of Bristol suggests the scheme was used more in the most deprived parts of the region.
Average bus use increased by 32% during the scheme, this compares to a 56% rise in Lawrence Hill, and Hartcliffe saw a 130% spike, researchers found.
Musse, who is also a director of Barton Hill activity club, said she had heard stories of families using the scheme to visit new places.
“Someone was telling us they went four times in one summer to Weston, they’ve never been before because they can’t afford it,” she added.
“It’s amazing – that opportunity for people to explore the city they live in with less cost.”
The researchers recommended extending eligibility up to 18-year-olds, and extending it beyond the school holidays.
Neither of these ideas are currently being implemented because of the potential cost, though Godwin has previously indicated she would be in favour.