A bridge system is provided that utilizes foundation structures that are formed of the combination of precast and cast-in-place concrete. A method of constructing the combination precast and cast-in-place concrete foundation structures involves receiving at a construction site a precast concrete foundation unit having elongated upright wall members that define a channel therebetween, and multiple upright supports located within the channel; placing the precast concrete foundation unit at a desired use location; delivering concrete into the channel while the precast concrete foundation unit remains at the desired use location; and allowing the concrete to cure-in-place such that the elongated upright wall members are connected to the cured-in-place concrete by reinforcement embedded within both the cured-in-place concrete and the upright wall members. The bridge units may be placed before the pouring step to embed the bottoms of the bridge units in the cast-in-place concrete.