Bags, such as L-sewn bags and multi-substrate bags, are formed at least in part from an open mesh material that includes filaments that intersect one another. At least some of the filaments are composite filaments having a carrier portion of a relatively high melting point and a bonding portion of a relatively low melting point, the bonding portion of each composite filament being thermally bonded to other filaments at points of intersection. The material may be a non-woven fabric that contains at least two layers of weft filaments that may be bordered on one or both sides by a layer of warp filaments. When compared to other open mesh materials, the open mesh material disclosed herein has a superior combination of some or all of high strength, light weight, high dimensional stability, and openness. Also disclosed herein are methods of making and using such bags.