Since it's made of natural fibers, it might be intuitive to assume cotton is eco-friendly. But pretty much all assessments comparing bags agree that cotton totes have the worst impact. Cotton takes a lot of water to grow, fertilizing it leads to river and ocean pollution, and it is energy-intensive to convert the raw fibers to textile. For a particular organic tote, the Denmark assessment found that you'd have to reuse it 20,000 times to match the impact of a single plastic bag.
That really high number is based on an ozone-depleting chemical used in manufacture (which some have argued is an unrealistic representation of cotton manufacture). In terms of contributing to global warming, the same totes only needs to be reused 149 times. And, especially if you use if, for years, you'll still be cutting back on plastic pollution.
If you are interested in buying a cotton tote bag and want to keep your environmental impact as low as possible... Choose organic and recycled cotton reusable bags, or calico, an unbleached cotton material that undergoes less processing.