Bunny squeaks for an odd thing.

I have owned rabbits before and none of them have ever squeaked for any reason.

This rabbit, female English Spot age 4 months (not yet spayed.. wish to wait until she is 6 months) literally squeaks when I refuse to let her out of her cage (or so it seems). She will come up to the cage door when I come up to it, we touch noses, and then I turn around and walk away and she will sit up on her highn legs, push against the cage door and faintly squeak two or three times before pawing at the cage door and then go to lay down.

Is she begging to come out or is this aggression and she is saying "DO NOT COME BACK!"?
She does try to groom me every time I come up to the cage, hold her, pet her... Constant licking. (I know this behavior most likely will go away with age)

This behavior is very new to me. (I also never had a female bun).

Note: my bun gets 3-4 hours of free run time in an X-pen at night. On fridays she gets 5 hours because that is clean up cage day. I do spend some time with her in the x-pen but not a full amount (it's 4 hours and I have humans to care for). X-pen has boxes for her to climb on and hide in. She loves climbing. Hence her name "Ivy".

some bunnies are noisier than others.

Cute! It's not common for bunnies to be very vocal, but some are. It sounds to me like she is begging to be let out. Licking and grooming you definitely shows she likes you.

Definitely begging to be let out so adorable! My adult girl begs but she huffs instead of squeeking and she still licks when showing appreciation or of she wants me to groom her in return

So I guess females are more vocal?

They can be although I had a very noisy male once lol he grunted a lot he was territorial though. Sometimes they make noise when they want something, it's not common but every bun is different