Well, there are several Robert Wilson's listed in the Army, many of them in Alabama units. But, there is only one Alfred Bearden, and he's listed in Moore's Company, 4th AL Militia. Interestingly, there is also a Robert Wilson listed in that regiment, although in Co. "D". So, there is a possibility, at least, that these are your soldiers.

Co. "D" and Moore's Company were composed of "90-Days" men, called out for coastal defense in March 1862. These companies, and others of the regiment, were employed as a police force in Mobile, or they were used as garrison troops in the various forts around the city. The regiment was disbanded in the summer of 1862.