I am an Indian citizen. Also, I will be taking my bicycle with me back to the US in August. The price of the bike is around $1600 and it isn't sold in India.
This is too late for the original poster -- sorry! -- but since this is a Q/A site it's worth answering. The Indian customs for travellers booklet says
Used personal effects (excluding jewellery) required for satisfying daily necessities of life
are free. You can try to argue your bike is such but I wouldn't hold my breath.
Also, your allowance is 35 000 rupee which equals 487 USD. How much is a bicycle worth used if new it was 1600 USD? Hard to say.
If you feel it's much more than 500 USD then since you are temporarily importing a rather valuable good, the answer is an ATA Carnet. There are two companies in the USA authorized to issue them, Roanoke trade and Corporation for International Business. The base fee for a good under $10K will be 235 USD. You need to present your carnet outgoing to US Customs and when entering a country, go through the red corridor to show your carnet to the relevant customs authority.