How can I get my peer's ban score for my node?
Correct: there's no provision in the P2P network protocol for your peers to tell you what ban score they've computed for you.

Since each node connected to you separately computes a ban score using its own rules, there's no way for you to confidently know your ban score unless you have some sort of monitor that knows all the ban score rules for all the full nodes connected to you.  (E.g. the rules for Bitcoin Core 0.9.0, 0.9.2, 0.9.3, etc...)

You could get a rough idea by running a separate Bitcoin Core full node that connects to your node using the whitelist option.  With whitelisting enabled, Bitcoin Core still calculates the ban score and prints it to debug.log even though it will never disconnect because of a high ban score.