Not aware that he ever played it with Rainbow, but a great info. Blackmore back then liked a pick playing sound with a bass and a lot of presence zzzing, the Bird would have been too mellow, especially with Cozy taking no prisoners in the back. After Blackers fired him (allegedly for "not being a good enough bass player" after his predecessor and intermittent successor Craig Gruber had been criticized for playing too much), he was a while with Ian Hunter's Overnight Angels before the Wild Horses. He might have played 5the Bird with Hunter, it would have been a nice nod to overend watts.
What's Bain doing now? Drug issues got him fired with Dio the rumors were. Last I heard of him was when he auditioned for the Stones after Wyman left. Heard that he got quite far actually. Had they taken him, they'd sound quite a bit edgier today. Bain is no slouch on the bass (and his playing improved greatly on those early Dio albums), but not really an R'n'B (in the old sense) groover, his playing is always a little jagged.