Cloth diapering can be much more cost efficient than using disposables - including the cost of washing.
There are many types of modern cloth diapers, and the cost of diapering largely depends on the type of diaper chosen, as well as the brand of that diaper. Most types are sold with an organic option, which will also raise the price of the diaper.
There are more expensive versions of BumGenius that are AIO and are made of organic cotton, these are called BumGenius Elemental.
Fitted diapers are likely the most expensive option, as they are sold for specific weight ranges and will not fit a baby from birth to potty-training as many of the others have One-size options. Many fitteds do not have a waterproof outer shell, and also require the use of a cover.
All-in-2 or Pocket diapers (AI2)
The classic BumGenius diapers are a pocket diaper, and there are many cheaper options for pocket diapers, including but not limited to AlvaBaby, Sunbaby, and KaWaii.
gDiapers are an example of a hybrid, and are the most expensive of the hybrid diapers available. A cheaper hybrid option is the Flip System (offered by the Cotton Babies brand who also make BumGenius diapers).
Modern covers, such as the Thirsties Duo Wrap, allow for parents to use flats, prefolds, or fitteds very practically and for very little cost.
The most cost effective way to cloth diaper is to use flats, but those are certainly not a modern option. Prefolds are also an older diapering technology, but the new version of covers developed help to avoid the "plastic pants" that were so terrible 25-30 years ago. (Also, the Snappi helps avoid sticking the parents and baby with pins, making prefolds and flats a truly modern option.)
Other Cost Factors
We have a toploading HE machine that allows me to turn off the HE option. I wash our diapers in a conventional amount of water (they are harder to get clean with less water), and our water bill has only gone up about $4 per month. Our electric bill hasn't noticeably changed.
The biggest cost advantage for cloth diapering is seen when the diapers are used for a second or any concurrent children. For the second babies and beyond, you do not even see the upfront cost of purchasing the diapers. This allows a family to diaper a child for about $5-$10 a month which is significantly less than purchasing disposables.