Hyperventilating Bunny

Just last month, my parents and I adopted a new bunny. She is only about a year old and she's our first bunny, so we don't know much about them or their behavior. Something that has me worried is, when I've held her before, she seems to either start hyperventilating immediately, or interchange between normal breaths and hard ones. Even when she appears to be relaxed, and/or sleepy. I'm concerned that she may be afraid or unhappy being held. Can anyone please help me?

It's not unusual for rabbits to dislike being picked up and held, and so getting stressed and breathing more rapidly. Most rabbits hate being picked up(as it's something a predator would do to them) and very few rabbits actually like being held. I've ever only had one rabbit that liked being held and cuddled.

I would suggest instead of picking your rabbit up, to sit on the floor(or couch) and allow your rabbit to approach you to be petted. It's more comforting for them to have all four feet on the ground when being petted and getting head rubs. It also helps build their trust in you. Though usually if you do it this way, you have to wait for them to run around and get all their energy out before they are tired enough to allow you to give them head rubs, at least this is how my buns are.

You might want to take a look at this link on how to bond with your rabbit.
http://flashsplace.webs.com/bondingwithyourbunny.htm

I have done that. I've also held her just fine before. Some times she actually seems to enjoy being snuggly. I'm just wondering if, on the occasions in which she has these moments, if they are because she is scared or stressed.

Probably yes. My rabbits have all disliked being picked up to diverse degrees. Some tolerate it pretty well but I've had a rabbit who had a bad case of vertigo. He was a pretty friendly bunny but would completely panic whenever you lifted up of the ground (his case was quite bad: he would jump on things, always looking surprised to have landed and something, and not be able to get down because when he looked down he couldn't bring himself to jump).
Just make sure she only does this when she's held and that she doesn't have a respiratory problem.

Actually, I just read something that suggests that heavy breathing could be her attempts to cool down her body. This actually made a lot of sense, seeing as I often pick her up while she is taking a break from her play sessions.

That's true. If she is getting too hot, her respiratory rate will increase. You can usually check this by feeling the ears as this is how rabbits cool themselves(increased blood flow to the ears). If her ears feel really warm then she may be getting too hot if being held for long or having previously been running around, and needs to be put down so she can cool her body temp down by getting a drink, laying down, etc.