USA Business Account and Address needed
It's relatively easy to have a US business address, and we covered this topic with in this research article: Obtaining U.S. Business Address.
Bank account is a different story. As a result of the events of 9/11 and the new laws that followed it became practically impossible for foreigners, who are not present on the U.S. soil, to open a bank account. To do so you need to either visit the U.S. or look into alternative solutions (which, by the way, do exist).
You might find a lot of advertisements out there offering easy ways to get a U.S. bank account or even merchant account (which, by the way, requires Social Security Number). We found most of those offers to be misleading and defrauding, so I would recommend you to be careful with spending money on such dubious propositions. Most of those services promise checking accounts in major U.S. banks such as Chase, CitiBank, Bank of America, Wells Fargo, etc. We have researched those options directly with those banks' Business Banking departments and received replies similar to this (from Wells Fargo), quoting:
...Unfortunately the only option for a foreign company to open the account once they are able to provide full requirements for their business is to visit one of our locations in the United States for the signer requirements. Because they are non-US citizens Wells Fargo requires a face to face interaction in order to complete the account opening process.
Online banks we tried to approach required physical U.S. address where the company is located (not a virtual one) with utility bill in the company name as a proof. Bottom line, unless you can visit the U.S. I would suggest going with alternatives.
We have a research article dealing with U.S. Bank Accounts for International Clients, I invite you to read it. For most part, the easiest alternative solution would be to open a USD checking account on one of the U.S. banks in your country (most of them have branches abroad), and use it as the main bank account for your U.S. business, until you can visit the U.S. and open one here. This option would also make it easier for you to open a merchant account in the same bank, if you plan on accepting credit card payments.