Fort Bowyer was at the site of present day Fort Morgan near Mobile Bay in Alabama.
From this source:
Fort Bowyer was a small semi-circular fort built of logs and sand in 1813 and named for Revolutionary War hero Colonel John Bowyer. When present day Fort Morgan was built, Fort Bowyer was used as headquarters. Fort Bowyer burned in the 1830's.
A redoubt at the end of a tongue of land on Mobile bay called Fort Bowyer was imperfectly raised and garrisoned by 130 men of the second regiment of United States infantry commanded by Major William Lawrence.
The men were not artillerists. Their means were extremely slender. But Major Lawrence gallantly repulsed the formidable assault by land and water, which began there the invasion of Louisiana; though after the victories of New Orleans, he was at last compelled to surrender his fort by capitulation to the final hostilities on this continent [2nd battle]. [Source]