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All of the commentors above commonly menioned "바빠요." It could be a polite way to say it, but it can never be in a "formal" way of saying.

For example, to your customer if you say "바빠요," it is actually a rude way of saying.

If you are saying that you are busy to someone you need to be polite AND formal, you should say something like..

죄송하지만, 제가 지금 급히 볼 일이 있습니다.(I'm sorry, but I am currently occupied with an urgent matter.)

Mostly we add an expression of apology. It doesn't mean you did something wrong. It is just an expression of excuse for making the person to wait for you.

바빠요 is correct grammatically but I have heard 바뻐요 is widely spoken by Korean too. 

으 verbs conjugate irregularly :) look at the last vowel, not including ㅡ. It is ㅏ so add 아요.

There are not much of difference 

when you say fomally or politely,

바쁘세요? 바뻐요? sounds right