Baker's yeast is capable of fermentation, so it can certainly produce alcohol.
In 1926 it was reported in the Canadian Medical Association Journal that bread can contain between 0.04 and 1.9% of alcohol. This is just a short report, not a full scientific paper.
In "Ethanol Content of Various Foods and Soft Drinks and their Potential for Interference with a Breath-Alcohol Test" the alcohol content of certain kinds of bread are reported. The highest alcohol content is found in Rosemary's onion bread with 0.98%, and lower values for other kinds of breads.
So, bread certainly contains at least traces of ethanol, and possibly even rather significant amounts.