Our intact female Aby was inclined to bite for the first several months we had her. I think part of it was her being young and an Aby; we got her at 10 days old when she was thrown out, so that I'm sure didn't help with trust issues.
A couple of things helped with us: one was training ourselves to learn about her behavior, and the other was simply her maturing. She is very different than our 3 American cavies. She is hyper and much smaller. She only likes about 10 minutes of lap time, at 7 months old, and she could only tolerate about 3-4 minutes when she was little. We learned that she would change her chutting to a purr to a fast DUT DHUT when she was done, and then she licks once, and then she bites. So the key was to respect her limits and put her down for floor time or back in her pen.
She also needs a lot more floor time, play things, and a bigger pen then her fellow piggies. I think like a hyper dog she just needs to be able to burn off energy or it gets pent up and she nips. Also, she is very sensitive about the hair in her rosettes -- she will nip if you try to brush against the grain or anywhere below her shoulders. She loves chin rubs and if you gently rub in between her ears (on top of head). She doesn't like to poo or pee during laptime and gets frantic if she has to (whereas the others will pee or poo anywhere). I've only been nipped a couple of times in the past month, and that was when I didn't respond fast enough to her warnings.
The other thing is just that she is older and a tiny bit calmer. Though I can tell when she is in heat because she goes nuts if you touch her at all during that time.
None of them like being picked up.