re: Can anyone estimate the cost of converting a ditch to culverts?

You are typically required to have a permit. You will probably also not be able to just drop a pipe into the ditch and cover it. You will need to dig it bigger to accommodate a larger culvert that will provide proper conveyance of water.

All of this is to ensure that your project doesn't cause drainage problems upstream for the following issues:

1. Open ditches provide much better water conveyance and additional storage during rain events.
2. Pipe/culverts laid too high (invert elevation) can cause pooling upstream (mosquitos) and affect flow.
3. Insufficient soil coverage (especially if you plan to drive over it ever) can result in collapse and loss of flow.