Bonus shares are issued to shareholders as on a record date as free of cost by the company.
Those eligible shareholders receive bonus shares automatically to the credit in his /her demat account. Bonus shares can not be renounced but surely you can sell on stock market.
Right shares are offered by company for fresh subscripttion of shares by making payment at the issue price. Such RIGHT , you can renounce in favour of other interested person to subscribe to shares at a market prevailing price for such renunciation.