Yes. The results speak for themselves. Jurisdictions that have instituted similar bans have seen significant changes in the amount of bags used and the problems they cause.
One year after LA County implemented its bag ban, there was a 95% reduction in the distribution of all single-use bags, including a 30% reduction in paper bags. San Jose has seen an 89% reduction of plastic bag litter in storm drains, a 60% reduction in creeks, and a 59% reduction in city streets.