This study presents a new approach to bidding for Gencos participating in a competitive market, which takes account of both the uncertainty as well as the cost characteristics of the generating units in an effort to make a reasonable profit from the operation. The price uncertainty is accounted for by representing the price appropriate statistical distributions. Such statistical representation of market price is utilised to enable a Genco to be successful in a bidding process with a specified degree of confidence. The screening curve commonly used in planning and operation of generators in traditional operation of power systems to characterise the economic merits of the generating units are utilised in this study to account for the costs incurred by the Genco in its operation and establish the desired level of bidding success in the market place. The logical development of the strategy is illustrated by implementing it for a Genco with three generating units, which are chosen to have competitive cost characteristics with respect to the market price. The results of the Genco operation are presented to illustrate that the methodology succeeds in securing reasonable profit. The simulation is extended to illustrate how the accuracy of the price modelling is important to ensure better profits.