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

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It depends some ditches require 18" culverts while others require 48". Obviously there is a difference in cost.

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There is a HUGE difference in cost once you step up to 18" and 24" culverts.

Just for reference on Black Corrugated pipe:
15" Pipe - $9-$10/ft
18" Pipe - $12-$14/ft
24" Pipe - $18-$21/ft

Typically your drainage board will have a map of the area with drainage requirements. You should get this information through the permitting process.

Our parish will set the pipe or driveway culverts for $20/ft if you supply the pipe. They supply the labor and the dirt.

Our neighborhood requires a drain box every 80'... they add some significant cost to the project.