How can I expedite getting my bonus after having been in the Army Reserve for almost a year now?

Which type of bonus are you getting as the processing for them is a bit different (some are processed automatically and some have to be manually submitted). Regardless, your Career Counselor (ARCC)* should be the first stop as they can get insight.

If you haven't checked with them specifically, have them ensure* your reenlistment was properly processed through the Retention Management System (RMS). If you don't have a local Career Counselor (or don't know who it is), contact the respective ARCG Battalion's operations cell* and they will connect you

If they can't determine what's up, then they will kick it up to the Area Leader who will forward it to the Army Reserve Career Division (ARCD) if they likewise are unable to figure out the issue.

The ARCD will either correct the issue or they will tell your unit why it's not being processed.
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* Army Reserve Careers Group contact info - https://www.usar.army.mil/ARCG/ARCG-Units/
* ARCCs can check https://xtranet/usarc/g8/pay/Bonus%20Report/Forms/AllItems.aspx for bonus status. If it doesn't show up, they should follow the