I have one bridge spanning a wifi interface and a 4G modem (visible as ETH01):
I also have an Ethernet card connected to another local network. Here is the routing table:
default via 192.168.8.1 dev BRIDGE00
192.168.8.0/24 dev BRIDGE00 proto kernel scope link src 192.168.8.2
192.168.64.0/24 dev ETH00 proto kernel scope link src 192.168.64.75
Now, from a machine connected to wifi I can access internet through 4G modem just fine. But if I try to access anything on the other local network (192.168.64.0) then routing does not seem to work. The packet originating in WLAN00 gets forwarded to ETH01 rather then routed correctly.
BRIDGE00 has a statically assigned address 192.168.8.2, otherwise the 4G modem has its own DHCP, so the machine connected to wifi gets address from there.