You cannot choose to pay the cost (discard a card or egg) and then decline the bonus effect; the bonus is always tied to the cost. The rulebook specifies that the bonus conversions are optional, but if you choose to pay the cost, you must take the associated benefit.

• On page 7, for the "gain food" action:

  "If the slot where you placed your action cube shows a card-to-food bonus conversion, you may discard at most 1 bird card from your hand to gain an additional food. This is optional. When you gain this extra food, you must choose among the dice that are remaining in the birdfeeder."
  This means the entire conversion (discarding a card to gain food) is optional, but if you discard the card, you must gain the food.

• On page 9, for the "draw cards" action:

  "If the slot where you placed your action cube shows an egg-to-card bonus conversion, you may discard at most 1 egg from a bird on your mat to draw an additional card. This is optional. Remove 1 egg from one of your bird cards and return it to the egg supply."
  Again, the conversion is optional, but if you pay the cost (discard an egg), you must draw the card.

There is no rule allowing you to pay the cost and then decline the benefit.

Source: pages 7 and 9.

Source: Core Rulebook (pp. 1, 2, 7, 8, 9)