I don't have bags, but I do have some black under my eyes. The trick to applying concealer under your eye is first never rub it in. Use your wedding finger to pat the concealer in , trust me it works, then cover the concealer with a little darker shade cover up than the concealer is, maybe 1 shade darker. The concealer should be either your shade or one shade lighter than your skin. The best product I think out there for lightening the skin under your eyes is
Sephora: Shiseido White Lucent Brightening Eye Treatment: Eye Treatments
I have used this and it really lightens up that area and considering how expensive and how most of these supposed skin products work, I have found nothing comes closer to this product and the price is moderate.
Good Luck