Bridge device is used to aggregate different network segments. By bridging one computer host residing in one network segment can communicate to another host residing in another network segment. Bridge works at the layer 2 protocol, based on the destination MAC address, it forwards the packets. Switch is more practical device since it has more ports compare to bridge and works as the MAC layer.
However role of gateway is vast in computer networking and mainly in telecom network. It is used to connect different kinds of networks together. For example : PGW in LTE network which is the gateway between LTE network and Internet. When host machine is not aware about the destination MAC of target, it sends packet to its default gateway and gateway takes appropriate conversion if required and send packet to destination.