Leena, all PSU's i.e New India, Oriental , United India, National Insurance provide Pedal Cycle Insurance.
These policy covers damage or loss to your cycle and third party liability - a lot like how comprehensive car insurance policies work. Check out this link :http://newindia.co.in/Content.aspx?pageid=63
As for Private Insurers, I think premium manufacturers have direct tie ups with the Insurers like check this link out : http://www.firefoxbikes.com/BicycleInsurance.aspx
