I've actually thought about this while washing bags. Something about it just felt dumb to me, so I looked into it.
First surprize: Plastic takes a lot of more water to produce than I expected. It takes roughly 22 gallons of water to make one pound of plastic. (180 liters to produce 1 kg)
Second surprize: My tap water gets pump lifted 3000 feet and travels 336 miles, which uses about 2 megawatt hours of energy per acre foot... and that power comes from a coal powered plant!
Your math will depend on your source of water and your source of plastic, but I was able to zero out my environmental impact by growing veggies with the water I use for washing plastic. Most of my plastic comes to me in the form of big bags that contain (literally) tons of coffee grounds. I rinse them off in a tub of rainwater that eventually goes to the plants.
When I use the plastic to prevent soil evaporation, my primary use for plastic, the water I save is greater than the water originally required to produce the plastic... by a factor of FIFTY! This goes to show that the destination can often be more significant than the source.
These next five paragraphs have been added for the benefit of those who disagree with the use of plastic in conjunction with plants. Firstly, I store custom mixed soils and soil ingredients in plastic bags until they are ready to be used. There's a reason why potting soil always comes in plastic. With the proper moisture level, such soils can remain alive and active, and can even increase in fertility. It sure beats having to hose it down periodically, or every day as would be the case where I live.
At some remote desert locations, plastic can be the most precious commodity for miles in every direction because it can produce and purify water through distillation, but when it's integrated into water collection and retention you can achieve stunning results. Even sandy soils in arid climates where nothing will grow can be restored with a little plastic if you form a bowl shaped bottom to your planting hole to make a deep pocket of moisture similar to a wicking planter or a mini cistern. This can create a toehold or springboard for diverse life and microbial generation in otherwise sterile environments allowing the establishment of drought resistant native plants.
Naturally, if you live in a wet climate with poor soil drainage this would be counterproductive, but I've seen scrap plastic being layered in a mound formation to shed water away from plants that are in danger of rotting from over-saturation. In the sweet zone between these two extremes you will be sure to find plenty of nearby organic material to stabilize your soil moisture which would be vastly superior to plastic, but you may also consider using old plastic bags to stave off a light freeze. They make a handy little tent or mini greenhouse over small individual plants and can be used year after year to extend your growing season.
Even after reusing my plastic in all these ways, I still end up with a surplus of small bags from the kitchen that I don't want to clean. I plant trees in them when I'm running short of small containers, and then pack them side to side in crates to make them easier to move. The bags prevent the roots from getting tangled until they are ready to be installed. If you do this, make sure to provide plenty of drainage holes or your trees may rot.
I realize that I'm getting a bit far afield from the original question about washing plastic bags, but the main point should be summarized in the statement that the ultimate destination of plastic can often redeem it from what many consider to be its inherent evil. A carefully washed plastic bag these days may end up in a landfill or a smokestack due to unscrupulous recycling programs, but when it's used creatively by you, the individual who considers and weighs its value against the value of water, it can be transformed from a waste product to a valuable resource that can help restore the planet, especially in regions where water is the greatest concern.