It sounds like you are describing a drilled well. An 8” bit is used first to drill down to bed rock. The water comes from cracks in the rock and not from the soil above the rock. The 8” hole is drilled down into the rock deep enough so the casing can be pressed into the top of the rock. The first section of casing has a drive shoe on the bottom end. The drive shoe protects the end of the pipe that is driven into the bed rock by the drilling rig. The casing seals off all surface water above the bed rock. After the casing is set then the 4-6” bit is lowered into the casing and is used to drill a 4-6” diameter hole into the rock. This is a better quality of water. The well driller goes as deep as needed in the rock to get enough water. So 70 ft is not far at all, I would have asked him to drill deeper. The 8” section is not as hard to drill because it is mostly in the soil but you have to pay for the cost of the steel casing. The 4-6” hole does not have the cost of the casing but drilling in the rock wears out the diamond bit and just takes more time. Some states require the casing to be grouted 20-35 feet deep. An over-reamer, looks like a giant hole saw, goes over the outside of the casing and bores down usually 20 feet. The annular space is about 2” around the outside of the casing is filled with concrete. The grout prevents surface water or contaminates from running down the annular space around the outside of the casing and seeping into the well at the base of the casing.
I'm not sure what it cost per foot these days. Normaly you would be charged so much per foot for the casing part of the well and usually a different price for the bore hole in the rock. The grout and slab would be extra. The cost can go up if the well is in a bad location etc.