So I ended up placing a packet sniffer between two computers. Here's my results. If this sounds out of whack, let me know.
The entire conversation (connection, message, closing, etc) was 3551 bytes.
A single bytes message with a 0 (zero) as a message was 320 bytes.
There were a few attributes we need to pass, so the 320 bytes might be slightly higher or lower than what you have, depending on what you're adding to the header.
Hope this helps someone.