Can a US lawyer represent me in Bermuda?

The simple answer is no.  You must find a lawyer in Bermuda to represent you.   I'm sure you can do a search and find one who handles these cases.    Sometimes, however, you can sue in the USA with a US attorney if you are injured in a foreign country.   For example, if you fall, or are a victim of an assault in a Mexican Hotel, owned by a US Company you can sue here.    The choice of law will probably require Mexican law to apply.    Also, if the Mexican resort is not a US company, you still may be able to sue in the USA if they used a US travel agency and directly marketed to you in your state.   It's an interesting choice of law issue.   The NJ Supreme Court recently ruled that an auto accident in South Africa could be brought in NJ because the plaintiff lived in NJ and the responsible driver worked for a US company.