She is confident enough now to tell you she is scared rather than just freezing
Guinea Pigs are prey animals which means they have a huge prey instinct, some piggies have this stronger than others.
We had a biter in Vimto, she used to bite because she was so very scared of us. Some piggies while fine in the cage and interacting on their terms with you but when on laps feel a vulnerable, the bites are her way of telling you she does not like it. I used to get actual snaps off Vimto and she would draw blood too
She was just a very scared piggie and felt vulnerable on laps, she didn't appear frightened (but obviously was) but she was confident enough with me not just to freeze and it was here way of saying 'please put me home i don't like this'.
Can you feed her in the cage veggies? Will she take food off you?
My advice would be to start trying to hand feed in cage to build trust. Start off putting some nice veggies to your piggy when they are in their hidey, and walk away, after a few times offer the food in the hidey by holding it - if they take it great - if not just pop it down in the hidey. Keep doing this till they take from your hand hopefully they will take it off you as you hold it in for them... after a while try offering it a little further from the hidey so they edge out and take it from you.
You'll have to do this for a month before attempting lap times again we then attempted laptimes. We worked at it and would take her out for 30 seconds then pop here home, we did this 3 times a week for around two months, then slowly increased it up to 5 mins via 30 second increments . Each lap session she'd have a sprig of coriander.
But some piggies really hate lap time and we as owners have to respect that, we'd all but gave up with Vimto and used to interact at the bars with her in the cage rather than lap times but by the time she hit 3 she was much tamer
One more thing use something like this to catch her, really takes the stress out of picking them up... the issue is you scare pigs by catching them which automatically sets them up to be frightened and stress at lap time