In The Expanse season 2 finale, Avasarala's bodyguard tells Bobbie that they have brought along her power armour in their skiff. When Bobbie crossed over to UN lines seeking asylum she wasn't carrying it. There is no question of the MCRN giving it to an absconder. So, how did they (Avasarala et al.) get it in the first place? Is it explained in the books?
It has been given/lent by the MCR to the UN for examination
In episode S02E09 The Weeping Somnambulist, the representatives of the Mars Congressional Republic have allowed access to the Bobby's power armor.
This is Marine Gunnery Sergeant Roberta Draper. She will be giving you her account of the battle. And in the interests of transparency, you're welcome to examine her power armor as well.
Furthermore, in the next episode, S02E10 Cascade, it is mentioned that the power armor is still in the possession of the United Nations.
TECH: Our analysts confirmed that Sergeant Draper's power armor was subjected to massive concussive and incendiary forces. And the suit's internal data logs, as far as they go, are consistent with the MCRN's account of the battle. The Martians wouldn't have given us the armor if it were otherwise.
After these events, it has not been stated that the armor has been returned to the MCR, therefore it has to be assumed it stayed in the UN possession. This would explain why Avasarala, as a very high-ranking UN official, was able to have it transported with her to the meeting.