Harvesting Sunflowers

So I am not sure how to really do this, but I felt like the sunflowers should have bags over them to keep the birds from eating the seeds and to catch the seeds that ripen and fall. So I put plastic bags over the heads of the sunflowers. I am starting to think that it wasn't the right kind of bag. I mean, the water can't get out too efficiently with the bags over them like that and so I am debating if I should trade the bags out for old bandannas / fabric scraps, or just make a few hole punches in the plastic bags to let air and stuff out. Hmmm.

Any thoughts?