You'll first need a US account to deposit into but if you are just wanting to get some US$ to take a bet on the exchange rate falling back to exchange it later on you could just shop around the different banks who will all remarkably have much the same exchange rate and then just buy some US$$$.
The only problem with that is you also always have to contend with the buy/sell spread and do check at the banks and you'll see how much you lose.
For doing an actual transfer there could be a slight variation between the banks and various currency exchange dealers like Forex and some may have slightly cheaper fees but the actual bank fee for a transfer is quite minimal and if you have the facility on your account here and an account in the US with the bank there set up too you can do international transfers online yourself, a few years since I have done one but the fee used to be just $20 irrespective of the ammount.
Each bank needs to have a Swift or IBN code and if you have the account details/numbers you can do it within a matter of minutes from home.
If you are travelling shortly and want to avoid the fee you could just buy some US$$ and take it in cash, there being some limits to that, A$10,000 here and above that it needs to be declared and I'd expect the US to have something similar, all about controlling money laundering.