Jordan didn't need bird and magic to win - he beat 'em.
Unpopular opinion: and yet if Magic and Jordan teamed up like Curry and Durant, Bird wouldn't have won jack. He'd be lucky to have a single ring. Just the times we live in.
Bird won rings in 1981 and 1984, before MJ was in the league. That 1986 team was one of the best if not the best team in NBA history and Jordan was injured and barely played that year.
Long story short, Bird's three titles would have been safe from a Magic/Jordan marriage.