Well first off, we are presuming that there is a problem that needs resolving, and from what I read in the article linked by Akiko, there isn't a consensus that there is a problem, or at least one as significant as some would have us believe.
There isn't even a consensus that the Earth is round.
The only consensus that matters is that of those who honestly and objectively study the question at hand.
There is nothing preventing you from doing this. It's not hard. You don't even need to become an activist. Environmental concern is not a binary switch from 100% treehugging hippy to 100% sociopathic corporate stooge, where you choose one or the other with no ground in between.
Now I'm no scientist or researcher, but I'm not of the opinion that plastic bags are going to be the end our world as we know it.http://www.bbc.co.uk/news/science-environment-10781621
I could alternately respond with 'how is that sentence relevant', but yes, humanity is doing mass extinction level damage to the biosphere, of a sort not seen since the Permian-Triassic boundary.
We're also in the rather unique position of actually being able to mostly stop it.
But there is no 'private sector' solution.
Additionally, our first knee-jerk reaction when presented with a problem shouldn't be, in my opinion, to turn to the government for a mandate, tax, or other corrective action. By market based solution I don't simply mean a monetary one, but one that comes from the private sector.
How would a private sector initiative clean up an ocean?
It is in the private sector the best solutions come from. Again, my opinion.
This is demonstrably false.
Name one private sector initiative that created a better worldwide network than the Internet. This one is pretty egregious. Prodigy. Compuserve. AOL. None of their efforts hold a candle to the Internet.
Name one private sector initiative that manages water resources better than the USGS.
Name one private sector initiative that landed us on the moon.
You can have an opinion otherwise, but these are feats that have never been matched, by anyone else in the entire world, ever. The rest of the world, combined, dreams of rivaling them.
These do have something in common, however - they are projects specifically for the public interest and benefit.
Now what might be a solution that doesn't involve the government? Perhaps interest groups campaigning to the corporate entities to either change their offerings of bag types, or otherwise offering an alternative. Also, entrepreneurs selling and marketing reusable bags and promoting the concept themselves.
I imagine this was actually lobbied for by retailers as well as environmental groups. The optimal solution is for everyone to carry as few types of bags as possible, while also making sure that no other retailer can offer the 'convenience' to try to undercut them.
I don't suggest the government never have a part to play, but it shouldn't in my opinion be the first go-to option. In most cases, it should be the last. There is a reason we have state rights, and a reason we have a constitution, and a reason our government is formed the way it is. It's not to consolidate power and decisions in one or a few entities. I would think liberals would appreciate this concept, after all. This is simply my opinion, and not a judgement upon how other people see government's role.
And there is a reason the promotion of the general welfare is explicitly laid out in the Constitution.
Even then, it is a 220 year old document whose authors had no comprehension of the profound advances humanity would make, nor could they and nor can we blame them for that. We have top cope with the advances that they did not foresee, though they did in fact see advances would come that ought to be accommodated, as Jefferson himself noted.