I own a vacation house in the Bahamas. I'm a us citizen. I purchased the land in 1994 and built the home with after tax dollars on income I had earned in the US. If I sell the property, will I owe taxes on the sale, and if so, to whom?

Yes, for sure you owe long-term capital gains taxes to the United States.

You MAY owe taxes to the government in the Bahamas, but those taxes will likely be collected at the closing and can be used to offset some of the taxes owed to the U.S.