Hay is only dried out grasses and weeds, nothing more.
Any hay will work, as long as there's no poisonous plants mixed in.
You can easily go outside, cut regular lawn grasses, dry them out on the porch and then store it in a cardboard box.
If you are feeding a proper and quality pellet food, then it will be made mainly of alfalfa, so adding more alfalfa hay is not a good idea. Using other kinds of hay is much better and evens out the diet. You can buy 50# square bales from some farmers, there's many kinds out there. "Horse quality" is usually the better and more carefully made hays. Oat, timothy, clover, orchard, pasture/grass mix and so on are all fine.
Actually, clover hay is a no-no for adult rabbits - like alfalfa, it's a legume hay and therefore shouldn't be fed to adult rabbits. Any horse-quality GRASS hay is suitable for rabbits, though (mind you, with "cereal" types like oat, wheat, rye, etc. the seed heads would need to be removed before feeding because the excess carbs and calories can cause problems). Horse-quality is important because hay for cows can have things like mildew (or maybe it's mold, I don't remember exactly) in it that would make a horse or rabbit sick.
Lawn grass can potentially work... it needs to be hand-picked (not cut with a lawnmower or anything) and come from a lawn that you're sure hasn't been treated with pesticides or fertilizer. This tends to be impractical because of the volume of hay rabbits eat, though.
That picture is too small for me to really tell what it is... but as long as it's a grass hay, it's fine. Where did you get it from? (That could help us figure out if it's the proper stuff.)
If you have any feed stores, livestock supply places, etc. near you, then they'll almost certainly sell bales of hay for horses. If you tell them you specifically need grass hay, they'll know which of their hays fall into that category. Bales from feed stores are actually the best way to go (unless you have super-picky bunns like mine who won't eat it) - that stuff's almost always fresher and better than pet store hay and it's a fraction of the cost. I know around here, you can get a 50-80 lb bale of hay for around $8-15 depending on the store and the type/cut of hay.
A bale can be stored for a year or more as long as it's kept clean, dry and insect free. I bought two half-bale bags from
http://www.tackwholesale.com/bale-bags-c-11.html (I went with that instead of a full-bale bag because the half-bale bags are easier to move around and can be stacked to take up less space). Alternatively, you can use a rubbermaid type storage bin or even unscented large plastic trash bags. If you bring bags/containers to the feed store, they'll typically split up the bale and package it for you free of charge.
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