Wait until May 4th comes and goes without sign of your refund and then contact the bank again, is all I can say.
Usually the IRS' estimates for these sorts of things are spot on the money, at least with my bank. They said I'd get my refund on the 4th of March, and that's when I got it...although it hung around in my "pending transactions" list for several days before that and didn't show as cleared until the 4th on the dot. (Not sure about your bank, but mine lets me see what transactions I have pending for all my accounts online. If yours does, you could try checking that and see if it shows up there.)
Also: the IRS does refunds every Friday. Depending on circumstances, your refund might not have initiated until late in the day on Friday. Absolutely no transactions are going to be processed on the weekend. It's very early in the business day yet (at least where I am) on Monday, so it's likely it hasn't been processed yet, or is just starting to process. I know you want your refund, but do be patient.
Try checking your account after noon today, or maybe even tomorrow morning.
Also also: keep in mind that you filed your return near the end of tax season, and a lot of people likely did the same. It may take longer than usual for everyone's refunds to process through completely.