Is there a way that I can set up my account to have my customers pay for services rendered in dollars directly into my bitcoin account via an online electronic funds transfer from their bank account?
BitPay appears to have an all-in-one solution that allows you to set up a store checkout in a lot of different currencies that will be handled through the use of Bitcoins. As I don't have a hands-on experience with that, I can't vouch for how the system works.
Another convenient way of setting up a payment system would be to use BitInstant which allows a user to quickly convert cash into Bitcoins through a variety of ways. It does not appear to be as automated as BitPay though, and you would have to handle your own payments.
Lastly, you can encourage your users to get their Bitcoins through more traditional means, such as the use of Bitcoin Exchanges. This option also requires you to handle the payments by yourself.
You can accept payments through OKPay. The funds received can be used to purchase bitcoins at several exchanges which accept OKPay transfers (including Mt. Gox, and others).
In the U.S., most consumers don't have "bill payment" where they can push an ACH transaction to any arbitrary bank account number. There are several intermediaries which offer a bill payment option for businesses such as utilities and other businesses in which the funds are "pulled" from the customer's bank account.
Smaller businesses can accept the "customer push" payments capability by accepting PayPal, but the problem is those PayPal funds aren't easily moved to Bitcoin exchanges. As a result, Dwolla becomes a good alternative -- as Dwolla funds received can be easily moved to Bitcoin exchanges.