A major component of Dr. Bryson's research is to discover the ecological range of invasive weeds (especially recently-introduced non-native species); to determine the long-term effects of invasive weeds on crop growth and yield in various tillage production systems; and to develop methods of control for these weeds. Other research involves studying shifts in populations, biology, ecology, and reproductive ability of non-indigenous and native weeds in agronomic, urban, and natural areas.

He has developed best management strategies for troublesome weeds such as bermudagrass, purple nutsedge, hemp sesbania, tropical soda apple, and texas gourd in row crop production systems. He developed a system for large-scale crop production of a potential crop, annual wormwood, that produces a natural compound with anti-malarial properties. Dr. Bryson has also characterized the competitive effects of hemp sesbania in cotton.

He developed a technique and determined the rain-free period required for several postemergence herbicides currently used in crop production. This information allows farmers to maximize herbicide efficacy by using weather predictions and to minimize off-target movement of herbicides. Dr. Bryson has characterized morningglory species growing in row crop production systems for tracking herbicide tolerance and resistance.

Dr. Bryson is an authority on the identification, ecology, and biology of the sedge family (Cyperaceae) and the prickly nightshades (Solanaceae) in the southern United States. He has determined the ecological range, growth parameters, and/or reproductive potential of several non-native invasive weeds including deeproot sedge (Cyperus entrerianus), brown flatsedge (Cyperus fuscus), and tropical soda apple (Solanum viarum).

He is the curator of the USDA-ARS Crop Production Systems Unit's herbarium (SWSL), which serves as a repository for vouchers for research projects and floristic studies. Under his supervision, the herbarium has grown into one of the most diverse collections of weeds in the South. Vouchers from research on cogongrass, Johnsongrass, morningglories, purple nutsedge, and tropical soda apple are among the important sets of weed vouchers in the collection and document research by pioneers in Weed Science, e.g. Chester McWhorter and Gene Wills.