If you use a bike box/bag to transport your bike there is a very good 24 hour open left luggage office - prices vary depending on size but i paid 126 euros to leave my large suitcase for 18 days - sounds a lot but at least the bike was well protected for the flights - a soft bag would cost significantly less and at least you don't have to carry said bag around on your trip.
You can ride away from the airport on dedicated cycle tracks almost from the terminal doors - my advice is to take the route to the right towards Zeppelinheim (there is a nice little Zeppelin museum at the rathaus which is worth a look if you get a chance) which very quickly gets you away from the traffic.
Of course you can catch a train almost directly from the terminal too if you are travelling further afield.
One of the best bike/airport experiences i can remember!