If you can dig a trench and lay in the water pipe from your property to where the road, is then the cost will be determined on how much of the road/area needs to be dug up by the water company to connect you to the mains. Prepare yourself for a large bill
If you want them to dig the trench along the bridleway as well then you really are talking loadsamoney. If you can't do the trench yourself then get a friendly farmer neighbour/someone with a digger to do it for you.
When we connected to the sewage mains in London (involving 3m long trench in a pavement) cost nearly £8000 and that was in 2001. OK sewer connections are a bigger task but the principle is the same.
Just give your water company a ring and ask them, they should give you a ballpark figure for a simple connection