How do I get the tier 10 enlistment bonus for 17C?

You have the have the E6 identifier. you get this by becoming a certain job role. Are you a 17C now? If so PM me and I can explain more.

Be aware that is not an enlistment bonus. That is a re-enlistment bonus, for those who are already 17C, and have an E6 ASI (alternate skills identifier) if you note the column. That is a specialized school only a handful goes to (you can look up what the E6 ASI actually is). I've been trying to get that training but nearly impossible as a reservist.