Are there any banks in Singapore that I can set up an account with to do ACH money transfers in USD$?

Cedric, thanks for your tips; I guess my situation is the other way around; I need to set up a bank account like your BAC account which you are holding; how did you manage to set up your BAC account?

You can use a broker that has a presence in Singapore (local SG bank account) then you can transfer SGD to the broker to change into USA

I actually transfer money to my Bank of America's account in this way.

1. Transfer SGD to Interactive Broker's SGD account
2. Get the SGD converted to USD (bonus the FX rate is good!)
3. After a few days, transfer the USD from my IB to my Bank Of America banking account

No fees and excellent FX. Just that I need a few days to wait, as the broker doesn't allow new fresh funds to be transferred out so fast.