Is this one network or two networks?

It's one network. The bridge "bridges" the two physical segments into a single network. A bridge and a switch are (for all intents and purposes) the same thing in that they operate at Layer 2. A switch may also operate at Layer 3 (a L3 switch), but when it's performing L3 operations it's acting as a router not a switch.

Broadcasts to FF:FF:FF:FF:FF:FF (255.255.255.255) are called limited broadcasts and are meant for every node on the same L2 network. An example of this type of broadcasting would be an ARP request.

Broadcasts to the network/subnet broadcast address (192.168.1.255 on the 192.168.1.0/24 network for example) are called directed broadcasts and are meant for every node on the same L3 network. An example of this type of bradcasting would be a NetBIOS Name Query.

1 network, there is a bridge between, which split the collision domains. The bridge splits one big network into two network segments. But it is still one network.

The thing that is confusing is the word "network" it depends on how you define network. Network can be a set of connected computers, but the internet is also a network.

In this case every pc is on the same broadcast domain so you can safely say that it is one network but it exists of network segments.