While it’s possible to spay a bird pokémon, it’s extremely difficult and could lead to complications that, in short, means it’s not worth trying unless the pokémon’s life is somehow jeopardized by being intact. That having been said, I’m afraid that’s about all you can do, anonymous, other than training your pidgey to ward off unwanted advances on her own and to avoid mating if at all possible. The only other suggestion I can make for this is to look into options for rehoming eggs in a humane manner, just in case.