Where your bank account is located does not determine the country the income is 'sourced' to. That is defined by where the work is performed - meaning, where your butt physically sits while you work.
Your country of residence would consider your income to be theirs to tax first. The US claims the right to tax it afterwards, on the basis of your citizenship (hooray! Only US and Eritrean citizens get such a wonderful opportunity from their government!). You have 2 options to avoid double-taxation (paying tax in both the US and the other country):
(1) Claim foreign tax credits on your US tax return, which basically just reduce your US tax bill (down to $0 if possible) based on how much tax you paid to the other country.
(2) Claim the FEIE, which basically removes the income from US taxation entirely.
Which option you choose has a bit of permanence to it, and can't be changed back and forth freely every year (there are some rules to follow), so make your choice wisely. If your tax rate is higher in your country of residence, then option 1 can be preferable, if a little burdensome. This is because unused FTC's can be claimed for up to 7 years down the road. This can help under various circumstances, primarily if you ever earn higher than the FEIE, you could still fully eliminate your US tax liability by claiming up your unused FTCs from prior years.
FTC method can be a bit more cumbersome, but could be worth it as well. Good luck with your double filings down the road!