Borders "contain" a design. While I am a huge fan of borders to frame most quilt designs, Bargellos are the exception.
To me, Bargello patterns inherently resist containment. They are a snapshot of a pattern that goes on forever.
If I were you, I'd add nothing more than a binding that doesn't call any attention to itself. FWIW, I've made ~10 Bargello quilts, and that's how I've finished them. No regrets!