Yes a small study in the UK found that having a glass of beetroot juice each day improved speed and time over a set distance on a static bike.
Making Beetroot Juice
They speculate that it is the nitrates present in beetroot that helps. Nitrates cause dilatation of blood vessels which increases blood flow to muscles, bringing more oxygen for better efforts.
It is early days and more studies will be needed but you can bet that if accurate there will be a boom in beetroot juice sales.