I recently adopted a 2 yr old french lop. The previous owner told us how sweet and friendly she is. Though she is friendly with us she climbs on us and will lock and nip at us constant. She'll lock our skin but she nip us through our clothes. Does she not like us? Also the previous owner said they could always pick her up. She barley ever let's us pick her up
Nipping could be a sign of a few things.
You mention that she licks your skin - she may like the taste of the salt that naturally excretes in the oils in our skin. Does she have a salt lick?
She could also be trying to get your attention - what's happening in the context of the nip? Is she climbing on you? Is it feeding time?
When she nips you, what do you do? Occasionally mine will nip me, especially when he gets excited. He's not purposely trying to hurt me, he's just excited. I make a loud noise and make a motion - a jerk or jump - to let him know he hurt me, and he'll back off. Do you do something similar?
As for picking up your bun, you mention that this is a recent adoption. First things first, don't force picking her up. She's getting used to you just like you're getting used to her. Prey animals (sadly bunnies are a prey animal in the wild) typically like to keep all four feet on the ground. Instead of picking her up, get on her level and let her check you out. Let her climb on you... smell you... nose bump you... get used to you. She may just be nervous and need time to familiarize herself with the fact that you are not going to hurt her.
Hope this helps. Best of luck.