William Bennett served in Captain Isaac Van Horn's Company of the 27th Regiment of U.S. Infantry (regular army). The company was formed in Muskingum, Coshocton, Guernsey and Tuscarawas Counties, Ohio.
The 27th Infantry was a one-year regiment formed on 29 Jan 1813 and disbanded on 12 May 1814. Those men who re-enlisted after 12 May 1814 were assigned to the 19th Regiment of U.S. Infantry, another Ohio regiment.
Bennett received a land bounty of 160 acres under the Act of 1850. He could claim any federal land. Since he died in Guernsey County, he probably sold his land warrant to another person or claimed land in Ohio. A Ohio land deed would state if he used a land warrant from the military.
If you wrote to NARA for his papers and stated that he was in the militia, this is probably why they couldn't find any records. He was in the regular army.
General Society of the War of 1812