Bluetooth transport seems to block connections over other transports
I have no hard evidence for this claim, only anecdotal evidence. Mostly I noticed this when adding contacts. Even though both devices could connect just fine over the LAN, they wait until finally they manage to establish a Bluetooth connection. So adding contacts takes quite some time (and can even fail).
Now, I noticed that when sending messages and devices are connected via Bluetooth, the messages are not sent until the Bluetooth connection can be established. So I just disabled Bluetooth one one device and got the messages delivered instantly over the LAN transport.