I opened a business bank account at Bank of America in Wilmington, Delaware. My LLC was formed in the same state, Delaware but I think it doesn't matter. It was flawless, no documents needed about nature of my business, everything took around 30 minutes.Have you been able to open a personal non-resident account with ITIN at Bank of America or Wells Fargo?
May I ask what branch have you visited if you opened in person?
Because of regulations it's not possible to apply for a US bank account online as non us resident, you'd always need to do it in person.
Apart from the bank account you can also apply for a credit card which gives you nice benefits like 1.5% cash back or free American Airlines miles, I plan to get myself a card soon
Keep in mind that for a business bank account you need EIN as well as ITIN