Walking from the Baths you would return almost to marina at Spanish Town before taking the road to the Coppermine restaurant and then further to the end of the road and the old copper mine. Walking this is going to take a long time, and most of the stretch has no sidewalks (there are a couple of hundred yards in town with a sidewalk, the rest doesn't) and while there's little traffic what you do see running the roads will make you nervous. So instead of a 2 hour walk, go for a 10 minute car ride. I would also recommend getting a rental car since that will let you explore much of the island, ranging from the Baths to Leverick and you can also stop by some beaches (i.e. Savannah) which you wouldn't get to otherwise. I've always used Speedy's and have never been disappointed.
I'm not sure if LeaseOnLife has walked this before; although the path on Google
Maps he shows is the shortest route
it goes up and down a lot. I am a quick hiker and the walk from the top of the baths to Spanish Town alone is over 30 minutes. If you do that walk quickly in the midday heat you will need a good liter of water
. The Coppermine road also goes up and down short, but steep hills.