I did not come up with this, I saw it via /r/elderscrollsonline from Monsieur-Anana.
If you open up the crown store while bound armor is toggled and try to preview a costume it will toggle the bound armor visual while still leaving the bonus in place. After you close out of the crown store, the bound armor is not displayed, and you still retain the buff so you can show off your hard earned gear.
*edit* Looks like this is only for you, other players will still see the bound armor. Might be good for screenshots or videos though.