Grounding, bonding, water pipes, and your situation
The old-school way of grounding a house to the cold water pipe performed two functions, not just one:
- It grounded the house electrical system to protect it against induced lightning and static charges
- And it bonded the house plumbing to the electrical system to allow fuses to blow or breakers to trip if a wire faulted to the plumbing
Nowadays, Code requires us put in a dedicated electrode (ground rods or an Ufer for most folks) to deal with problem 1, and that's what you can do here -- running 6AWG copper from the main panel (optionally through a conduit) to a pair of ground rods spaced 8' apart and driven 8' into the ground will get you a serviceable grounding electrode in most areas.
You will still need to move the existing grounding/bonding wire from the hot pipe to the cold pipe and add a 6AWG jumper from the cold pipe to the hot pipe, though -- this will ensure that your piping is properly bonded to the electrical system so that you don't wind up with a shocking tub spout because the dishwasher shorted out.