What is a heat pump?
You almost certainly have one already. It powers your refrigerator or freezer, by cooling a gas (freon, usually). This generates heat which is dissipated through the metal fins at the rear of the unit. A ground source heat pump uses the same technology, but is designed to keep heat in not dissipate it. A sealed circuit of water comes into the house from the ground; as it passes through the heat pump it is cooled by up to 10 degrees. The heat from this cooling is used to heat the water in a specially insulated boiler which drives the heating of the house; the outside water goes back through the sealed circuit, warms up again in the ground and the process repeats itself. This technology was developed in Sweden, where building regulations require a heat pump in the foundations of every new house. It uses much less electricity than conventional heating, and allows you to have water at shower temperature all the time. The radiators are kept at a constant temperature, which means they never get hot but simply stay warm. When you want a hot bath you boost the water temperature, which takes half an hour or less.
How much does it cost?
The main cost is the digging needed to lay the pipes (more like plastic radiators) that are laid a metre or more deep in the ground. The boiler itself is big, because of the extra insulation, and may not fit a space designed for a conventional boiler. And you may need to instal water radiators around the house if they are not there already.
In my experience, because it is so easy to have a shower at any time, you find that your water consumption goes up, and if you are metered this means a bigger bill.