What's the simplest way to deposit BTC into US Banking account with minimal fees?
[...] I'm looking for some way to deposit my BTC into my US bank
  account. Is there any service that can do this [...] ?


In short, no.

Your US bank account holds US dollars, not Bitcoins.

You can sell your Bitcoins for US dollars, and deposit the US dollars into your US bank account, but you can't deposit Bitcoins into US dollar bank accounts.

Edit: I just found the Bit-Pay Deposit Card which claims to allow you to "Receive Bitcoins into your US Bank Account!"  So perhaps that's what you are looking for.  There's also a video about it.  Apparently "the fees are 2.99% which includes the currency exchange and the next-day ACH".