If you've only had him three days, he's still getting used to his surroundings. Give him lots more time to get to know you. One of the best things is to put them in a rabbit safe environment, get on the floor so you are at their level and let them explore. Bunnies are naturally curious and will eventually come up to you. Cinnabun, whom I've had for over a year, still nips at me if she wants attention or if I'm in her way or if I've done something she doesn't approve of and I haven't the faintest idea what it is.
Also, 6 weeks is just a smidge young for a bun to be away from their moms. How is his diet? What is he eating? What kind of bunny is he?

I agree completely with Cinnabun. My buns all still do the same thing. You may just being doing something he disapproves of or maybe he doesn't have enough toys he's interested in? My buns will tear and bite at everything if I don't have enough toys to keep them content and toys that they like! Bunnies can be pretty darn picky about their toys...

Also, 6 weeks is very young! Would love to see pics of your new little guy -- what breed is he???

Yeah, another forum I post on has already advised me about his age. I didn't realised 6 weeks was too young to separated from mum. He seems very happy and friendly though. He's on hay and a tiny bit of the same baby rabbit food they gave him at the store. He's also got a little water bottle of kitten and goat milk but he's really not interested in that - any ideas on how I can get him to drink it?

At the moment I have him out of his cage in my bunny-proofed bedroom for a couple of 90 minute spells during the day and then, late at night when he's sleepy, I have him out for a cuddle. It seems to be working. I think the nipping was boredom/restlessness.

He's a mix/cross and so far the most popular theory is some sort of lop crossed with some sort of rex. His colouring is the agouti coat, like a wild bunny.

Awwww -- he's absolutely adorable!

What a cutie! Just a suggestion: if you think your bunny is bored you need to nip this problem in the bud. Bored rabbits are destructive rabbits. Boredom will turn into tearing apart cages, carpets, and being very unruly. Make sure to provide your bun with lots of toys. Something as simple as a toilet paper roll can be fantastic. My bun always has at least 3 scattered around her play pen.

He's totally cute!

Those behaviors are totally normal and very common. Sometimes they just want you to move out of their way so they can continue with their digging project :-) He's very young right now, but eventually you can train him out of that if it's annoying you. My girl used to sit on my stomach, dig, and then bit my shirt (often biting my skin through the shirt), so I kicked her off of my lap whenever she would do this and make a yelping noise and she quickly understood that it wasn't allowed.

Many bunnies just love to dig, so provide him with an appropriate place to dig, like a box filled with shredded paper or a phone book with the cover removed.

He's a cutie!

Elrohwens right -- my girl still does the same thing but unlike her brothers where it's not allowed, she doesn't dig very hard and only nips a tiny bit so I don't mind when she does it. The yelping helps a lot with them realizing they've munched down too hard. Lots of yelping is how we got our first bun to stop taking such hard bites out of our body parts. My one boy is still a terror about it though. He's such a playful bun so you can't help but love him but he's always sneaking up and taking a big chomp out of my butt and then prancing away.

Concerning the not drinking part -- are you sure he knows how to use the water bottle?

Hello, I am a first time bunny owner too!When I got my Bunny she was about 3 months old, and she would give me small nips, and would only leave a light light pink mark on my skin. I looked aorund on the internet and it said that when a rabbit does that it means it is saying hi, look at me and pet me, or I love you.

D'awwwwww! That is the cutest little thing!

Thane does this quite often actually. He'd be sitting on my chest with me giving him snuggles and if I stop prematurely he starts digging at me and nipping. I just put him down and he runs off.