The UKEA study calculated an expenditure of a little less than two kilograms of carbon per HDPE bag. For paper bags, seven uses would be needed to achieve the same per-use ratio. Tote bags made from recycled polypropylene plastic require 26, and cotton tote bags require 327 uses. (Although they weren’t included in the study, one can presume that designer totes, made with leather adornments, metal, and so on drive the required number of uses into basically astronomical numbers.)Single use plastic bags come across well because they are so cheap and easy to make. If you use one twice, you are probably doing as well on your carbon budget than you would with any tote bag, since tote bags tend to be discarded before they are used 50 times.
Cotton bags are expensive, in both cash and carbon terms, because agriculture is just a less efficient way to make things than modern petrochemistry. By the time you have plowed, planted, fertilized, harvested, shipped, combed, spun, woven, shipped again, and so on you are using up a lot of oil.
Of course this is just the carbon budget side of things, and it doesn't take into account how many bags end up littering the landscape or dissolving into the oceans. Nor does it get into the deeper question of disposable thinking, that is, how our whole relationship with material things has been changed by our sense that they are all meant to be used for a short while and then discarded. But a hyper-rational approach to reducing CO2 emissions, for example via a steep carbon tax, would not move us from plastic to organic cotton; rather the reverse.