Tax AdviceWelcome to the forum! That's an interesting question and you will need to discuss your entire situation with your tax accountant or lawyer. There are a lot of offshore scams and real opportunities, so you want to be careful.
The good news and short answer is that since as a U.S. citizen you are taxed on your worldwide income, you are also able to claim business expenses worldwide and deduct them.
If you work in the business here, you may be able to claim income as earned income and qualify under the foreign earned income exclusion, which is now $80,000 per person. You also have to establish a tax home in Costa Rica or remain outside the US for 330 days total in order to qualify. This may not be possible for you immediately, but in the future may be something you should be aware of.
You will have to weigh carefully all the possibilities, since you would also have the option of incorporating in Costa Rica, which will allow you tax advantages for your business here, and may provide a shelter for your income. It may be possible that your income can accumulate in your Costa Rican company and you would not have to pay income taxes until you take profits as a distribution.
A lawyer some of the realtors use who specializes in forming IBCs may be able to answer questions particular to your case, read an article about forming a business in Costa Rica here:
Forming a Corporation in Costa RicaAnother possibility is to purchase the B & B using your IRA, the Go Dutch site has information about using this strategy:
Investing your IRA in Offshore Real Estate I have to make a disclaimer that I am not a tax counselor!

I am however a US citizen and I file taxes under the earned income exclusion, so I am aware of some of the available strategies as outlined above.
If you have further questions, feel free to fire away!