The Langeled underwater pipeline, carrying natural gas from Norway to the UK, is a bit longer than the Barbados-Surinam distance (at 1200 km), and cost approx. 2 billion USD adjusted for inflation. That's a really big-ass pipeline though, at 44" diameter. I guesstimate they could probably get this water pipeline done at about a hundred million USD.

Edit: Digging a bit further, subsea pipeline lay cost can be roughly approximated at 0.04 million USD per inch-kilometer (that is, multiplied by pipeline length and by diameter in inches) for 8"-24" pipe. Furthermore we can estimate that Barbados would need a flowrate of 5 000 L/s to supplement their water supply, giving an optimal pipeline diameter of 8". That means it would cost 942km * 8in * 0.04 million USD/(km*in) = 300 million USD.

What do you base that estimate on, given that planning, permits, work etc don't scale with the diameter of the pipe?

Actually, work does scale with the diameter. For lower diameter pipe, you can use a smaller, less specialized lay barge with less crew, the welding goes quicker meaning progress is faster, and you can fit more km of pipe on each supply ship.

Also, the cost of permits (called Right-Of-Way, ROW) is a very small fraction of the total cost, as is the planning cost. Materials cost for the pipe, OTOH, can be as much as 60% of total.

I guess the boat system can be moved around the world to meet demand. Unlike a pipeline that might not get used again for another 10 years.

Still I think the numbers seem off for a boat dragging water in bags for 6 days to be cost effective.

If you've never purchased pressure-rated pipe, you'd be shocked at the cost of even a 6m piece of 1" PN20 pipe.