I'm still not sure I understand, but it is sounding like you are looking for non-standard packet handling behavior.
A broadcast packet is generated by an application to a destination address that is the broadcast address for the assigned subnet and mask. 192.168.0.255 in your vlan1 above.
The switch will flood this to the entire broadcast domain just as the packet exists.
Devices will accept and read that packet and any application looking for broadcast traffic for that subnet will respond accordingly
If you create a bridge domain and bridge your vlan1 and vlan2, the vlan2 devices will see this broadcast packet addressed to 192.168.0.255 but will ignore the packet because the configured subnet on that vlan2 device is 192.168.1.x looking only for broadcast packets of 192.168.1.255
All the bridge domain does is allow the broadcast packet 192.168.0.255 to flood to all the connected devices. This will NOT change the destiniation address to the other broadcast addresses you are bridging togther. You would need some kind of packet manipulation and rewrite to do that.
Anyway, the reason your bridge domains are not connected is that you have created two separate bridge domains for your two vlans. If you do need to bridge the vlans into a single broadcast domain you create only one bridge domain and place both vlans and all the desired layer 2 interfaces into the bridge.
The IRB interface is only needed if you require a layer 3 interface in the bridge domain. You could still create your layer 3 interfaces using family inet on your physical interfaces on the SRX if you prefer.