Hay is dried grass! Do give her unlimited timothy or other grass hay, unless she’s under seven months. Then she should get alfalfa hay. When the first few pounds of hay I picked up at the feed store turned out to be not to my rescued bun’s taste, I picked tons of grass for him. The fresh stuff is better for them, anyway. You’re doing your bun a service. And remember the water content of grass makes it much larger in volume, so their tummies get full faster.
Give unlimited hay; I don’t know what you mean by three handfulls. Do you measure it and wait till she cleans it all up? Don’t. Bunnies will eat in the middle of the night, and she needs the hay there for her. It’s not “feed” like giving a dog a bowl of food. Put hay in her bed, they love sleeping on it. Put it in her litterbox, they love eating and pooping at the same time LOL
Make hay toys with paper towel rolls and egg cartons. Bunnies are foragers. In the wild, they roam about 2 acres thoroughly a day. They stretch, eat, run, eat, flop out, poop and eat, flop out, run the Bunny 500, eat and drink, flop out, eat some more. It’s never ending.
If you spread their feed out, they’ll eat when they feel like it, in the right amounts. I created a hay toy in the Toys section that incorporates most of my bun’s daily pellet ration. He loves tearing at the hay and finding the pellets, then making both hay and pellets scatter. Sometimes I scatter alfalfa pellets in his bedding hay. He goes crazy getting at it. His house is two connected cardboard boxes, and he loves alternating between chewing hay, finding pellets, and chewing cardboard.
I don’t know how you buy your hay, but if you’re measuring it, I suspect you’re buying very small quantities, like the pet store sells for ridiculous prices. Go to a feed store and buy half a bale, or find a farmer/horse barn on Craigslist who’ll sell you a full Hefty bag. I pay $3 per flake of hay at the feed store, which is about 2-3 lbs., and buy three-four flakes at a time. I keep the Hefty bag (contractor weight—very tough) in my storage room, and put a shopping bag of it on top of Borys’ cage, so I can replenish him any time. Which is constantly. Those pet store packages are only 24 oz., so you feel you have to conserve it.
Buns are messy, and you have to go along with it. When you do it right, there will be hay scattered throughout your home and in your underwear.
If the vet says Bella is healthy and she’s the right weight, then she’s doing fine with eating. I check my bunny’s weight daily while I groom him. I gently feel along his spine and ribs. They should be very lightly padded with flesh, and the hindquarters quite fleshy.