A commercially important alkaline protease, produced by Bacillus sp. RRM1 isolated from the red seaweed Kappaphycus alvarezii (Doty) Doty ex Silva, was first recognized and characterized in the present study. Identification of the isolated bacterium was done using both biochemical characterization as well as 16S rRNA gene sequencing. The bacterial strain, Bacillus sp. RRM1, produced a high level of protease using easily available, inexpensive agricultural residues solid-state fermentation (SSF). Among them, wheat bran was found to be the best substrate. Influences of process parameters such as moistening agents, moisture level, temperature, inoculum concentration, and co-carbon and co-nitrogen sources on the fermentation were also evaluated. Under optimized conditions, maximum protease production (i.e., 2081 U/g) was obtained from wheat bran, which is about 2-fold greater than the initial conditions. The protease enzyme was stable over a temperature range of 30-$60^{circ}C$ and pH 6-12, with maximum activity at $50^{circ}C$ and pH 9.0. Whereas the metal ions $Na^+$, $Ca^{2+}$, and $K^+$ enhanced the activity of the enzyme, others such as $Hg^{2+}$, $Cu^{2+}$, $Fe^{2+}$, $Co^{2+}$, and $Zn^{2+}$ had rendered negative effects. The activity of the enzyme was inhibited by EDTA and enhanced by $Cu^{2+}$ ions, thus indicating the nature of the enzyme as a metalloprotease. The enzyme showed extreme stability and activity even in the presence of detergents, surfactants, and organic solvents. Moreover, the present findings opened new vistas in the utilization of wheat bran, a cheap, abundantly available, and effective waste as a substrate for SSF.