Not sure where you're at... here, the grass hay sold at Tractor Supply is coastal, but I'm sure it varies depending on your region (assuming TS is national rather than regional, I don't actually know
). Hay should be 80% of their diet and they should have unlimited 24/7 access to fresh hay. Most people put it on one end of the litter box or hang it over the litter box in some sort of makeshift hay manger, since bunnies like to poop as they eat (assuming a litter box is used). If you don't use a litter box, then you can still make some sort of hanging/wall storage for it or you can put it in a plastic or cardboard box.
Hay is mostly just fiber, they can eat it non-stop and never get fat from it - it's pellets (and sugary treats like fruit and carrots) that can lead to obesity. Since bunnies are grazers, they actually need to be munching much of the time anyway. Bunnies tend to eat more hay if it's fresher, so it's a good idea to refresh it at least twice a day even if it's not all gone. Also, make sure she's not pottying on it (or if she is, that she's not eating from the same area she's using as a toilet). If you haven't been giving her hay, it may take a while for her to get used to the idea that it's food
.
Since straw doesn't have any nutritional value, you don't want her eating too much of it - while nothing in it would harm her, filling up on straw means eating less hay. If she's constantly eating straw and neglecting the hay, you can potentially use hay as both food and bedding and skip the straw (it depends on what the ambient temperatures are like - hay isn't nearly as good an insulator, so if it's below freezing then it's better to use straw even if she's eating it (lesser of two evils)).
It sounds like you've never bought a bale of hay before... it can be safely stored for a year or more as long as its kept clean, dry and insect free (storing it in cooler temperatures is better than warmer); I believe the same applies to straw. I typed up a ridiculous wall of text on hay storage yesterday, so I'll just give you
a link to that instead of writing it all up again
.