I think this is baby behavior. Baby animals of social species spend a big part of their day in close physical contact with their siblings. It helps their brain develop right. Rabbits are not lying close to their mother like f ex rats do, since mama bun only comes to feed them twice a day and doesn’t linger, but the siblings are together.

I don’t think you can give her too much physical contact. I just listened to a lecture held by an ethologist who said that you can’t “spoil” a baby animals (incl human) with too much physical contact or make them “dependent” on physical contact. Actually there have been scientific cross-fostering studies made on rats and primates that suggest quite the opposite. That animals who get lots of nurturing physical contact and care as babies grow up to be more resilient, less susceptible to stress and a lot less fearful than animals that have had “bad” mothers. I remember that from a MOOC on epigenetics as well.

It’s only for a short while that a baby bun needs this much physical contact: with puberty comes the need to emancipate oneself, become independent and fend for yourself (to an extent of course, they are still pets). This can happen literally over night with a bunny, esp a girl bunny. One day she might just act as if she’s afraid or you or really angry at you. We get lots of worried posts about this phenomenon here, but it is perfectly normal.

As for the sling or wrap, I’ve heard of those for baby buns, but I don’t know how to make one. We have one member (Ellie from the Netherlands) who has a special vest that enables her to carry around her bun safely, because he likes that.

I got my rabbit Bunita at 6 months. She was just what you described. Always following me everywhere and wanting attention. She never grew out of it but I had planned to bond her to my neutered male when I first picked her out anyway. Once they finally bonded She got significantly less clingy to me since she now had a partner who is always around her. It kind of makes me sad sometimes, I miss her following me and demanding cuddles, but I know that she needs company and when I’m off at work she’s lonely. This way she’s always got someone with her.
I would suggest maybe trying to bond her with another bun so she has constant company. Its a long and difficult process. It took us over 3 months to finally say they’re bonded but it’s worth it when I watch them cuddling and grooming eachother and knowing I couldn’t have been around constantly enough for her and now she’ll never be lonely!