Don't rely on JetBlue's website. If I was you I'd make a trip to the airport and ask how they (the baggage staff) want to see a bicycle packaged for air tranport. Your goal is to get it on the plane in Lima so it shows up at your desitnation (back in the USA?).

Another packaging option I've seen is building a cheap wood frame around a cardboard bicycle box, which makes it more rigid so the bicycle is less likey to get crushed. A little more spendy to make and transport, but good insurance to protect yuor bicycle.