I'm currently in the process of opening an LLC in the state of
Wyoming, after which I would like to open a business account in that
state, in Sheridan if possible.  However, I am abroad working on
organizing cooperation involving the business, and will not actually
be able to be present in Wyoming.

I would like to open an account without returning to the US but most
banks require someone to be personally present to open a business
account.  Bank of America seems to be an exception but they do not
have any branches in Wyoming.  Please help me to find  well known
banks in Wyoming that would allow me to open an account without
returning.  The account must include online banking capabilities and a
visa or mastercard debit card that can be used to withdraw funds from
abroad.

Of course, the bank wants  -must have- verification that you are "you".
The bank would probably accept notarization by a US consulate or
embassy, but in Wyoming not be familiar with this.  THey might also
accept verification by a branch of a US bank or US stockbroker in the
country you are in.