Roll up your smart clothes, or get one of those things for packing shirts so that they don't crease. Put them and your smart shoes in your panniers.
Take the journey steady so you don't arrive in a state of melt-down. When you arrive, ten minutes or so early, park your bike and ask to use the loo. Get changed and smarten yourself up, put your cycling kit in your briefcase or smart bag.
Do the interview.
Presumably, if you're offered the job, you'll commute by bike to do it. If you're asked about this, the interviewer is on dodgy ground, since how you get to work is none of his business - as long as you show up on time reliably. You could quite legitimately point that out, and ask if all the other candidates have been asked the same question (if they haven't, the employer is breaking the equal opportunities rules). However, you should be honest about it.
If it's a big place, there's no reason the interviewer should detect you came by bike, and anyway, it's irrelevant. Your performance doing the job is what's important.