As you want to apply online to Open Account in Bank of America, so I am providing instructions to open account online:

You should go on official website of Bank of America.

You will see a link to Open a New Account in right middle side on Homepage.

When you will click on that link, you will be on reach on this new page:



Now you have to choose account type. As you will click on Saving Type, so you will be on this new page:
promo.bankofamerica.com/chooseyourchecking1

On this page, you will click on Core Checking option and get a box to fill Zip Code and start process to open account.