I dont really know how the bags start.. but this may sound odd.... Hemroid cream takes the swelling down and minimizes blood vessels wich make for the darkness around ur eyes. If u put "Preperation H" on it should reduce it significantly

Significantly you say? I will have to try this immediately.

Should I apply once a day?

I did a little research on this and it states that;
Eye bags are caused by toxins.

Toxic foods such as MSG, hydrogenated fats, food additives
and so on will cause bags under the eyes.

Minimize all dairy products and you will see a difference
in eye appearance.

Drinks lots and lots of water

A good diet is the best cure and sleeping is a great healer too.

Next to reduce puffiness you can try masks, cooling eye-pads, and cucumber slices. But these measures are temporary.
Good luck and maybe posting pics of the before and after might help us to know if these measures work or not.
=D

Ok. I will defo drink more water. Regarding dairy products, I hardly have cheese, and the only milk I drink is with my cereal in the morning. Not sure about having no dairy products at all, as I'm sure I need some calcium.

I'll take a pic of my eyes soon (will add on this post via an edit). Looked in the mirror just now, and they are actually quite bad. Probably all the additives I eat, so will sort out my diet straight away.

EDIT: The camera on my phone does not have the quality required. And, looking at my eyes in more detail, seems I have both:
a) A small bag under each eye.
b) A small, blue streak (veins) running from inner corner of eye, following the contour of bottom of bag until it's almost in line (vertically) with centre of iris.

I might be stupid, and they may go hand in hand with each other.