I'm pretty confident that it's minuscule locally (these aren't European rivers: https://www.google.com/search?q=plastic+waste+river&tbm=isch), but I couldn't find solid data on waste that gets first exported, then dumped into a river.
Say it takes 1 year (probably less) from when a bag is created to when it gets thrown away. After it gets thrown away, it takes 100-1000 years to completely decompose. That means bags are entering the landfill faster than they are "leaving" via decomposition. That's going to be a problem. After enough time we'd just be like a malicious or poorly-designed AI that covered the Earth in plastic bags rather than paper clips.
Supposing for the sake of the argument you're right, that means we need enough landfill space for 500 years' worth of plastic bags. Is that really so much space that it's a problem?