You might be able to exhange your BoA items between your Horde and Alliance twinks in patch 3.3:

CM Wryxian – Then the good news is that, if you’re able to patiently wait for patch 3.3 you will probably be rewarded with the very thing you’re requesting. That’s right, we aim to implement the ability to exchange bind-on-account items between your Horde and Alliance characters in patch 3.3. Of course, as with anything not yet live (and even things that are) this is subject to change, but it currently remains our intention. Hope that helps somewhat, or rather, hope that will help somewhat. (Source)

Fingers crossed!

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1. Cross faction Heirloom items?
2. Blizzard’s Faction Changing… Will you?
3. Patch 3.3 – Cross Faction BoA Transfers Have Arrived
4. Patch 3.3 – 19 and 29 – Item Changes
5. Race and Faction Changes? What would you do?