Bridges are made of many materials, usually each bridge consists of more than one type of material, but the main goal of a bridge is that it supports the traffic load it is designed for. Asphalt isn’t structurally suited for creating a span, since it is flexible, and when it is heated, actually becomes plastic (in the sense it flows).
Bituminous asphalt pavement is not rigid. The asphalt holding the aggregate together is a thick, sticky fluid, kind of like really cold butter. It seems hard, but flows under pressure. It cannot support its own weight and has minimal tensile strength so is an unsuitable material for a bridge structure.
Portland cement concrete, on the other hand, is a rigid solid. It has excellent compressive strength. But it doesn’t have great tensile strength, so steel is embedded to provide the necessary tensile strength. Portland cement is an anhydrous form of lime, which is mixed with water to create a slurry that binds aggregate (sand and stone) together. Because it starts out anhydrous, the water in the mixture becomes part of the cement, creating chemical bonds between the cement and aggregate.
Concrete, on the other hand, when installed with appropriate reinforcing bars/mesh, can support its own weight plus an additional load. Most concrete bridges have steel supporting girders or prestressed concrete beams with steel cables and reinforcing bars integral to them, columns, pile caps, and piling, so the mass of concrete plus the traffic load can be safely supported.
Other bridges are built with wooden beams, planks, piling, and decking, or they are fabricated with steel beams, metal grating, cables, and other elements. Early in the bridge building business, bridges were built from cut stone blocks. These block structures rose up from the stream bed as stacked columns, then arched towards one another to span between supporting columns, a very simple, practical technique that served its purpose well.