Nipping, chasing and the squealing isnt bullying (bullying a sustained behaviour which sees the piggy become withdrawn and depressed, lose weight through not being allowed to eat enough), its normal dominance behaviours and the squealing is likely submission squealing - she is literally saying to the other piggies that she is no threat. It sounds dramatic to us, but submission squealing is an entirely normal thing for them to do.
Can you please confirm that you are carrying out the bonding in a neutral territory bonding pen?
It's just you mention her hiding under a ramp which sounds as if you may have put her into the original piggies cage. Adding a new piggy directly into the original piggies' cage will be seen as a territory invasion. I may have misinterpreted though.
The bonding needs to be done in neutral territory (somewhere where none of the other piggies see as their space - a bathroom or kitchen floor for example), with no hides and just a pile of hay. Bonding cant be done slowly - its all or nothing, one time event. They need to be put into a neutral bonding pen for several hours and seen through to conclusion (success or failure). If successful, they then all need to be moved back into their cage which has been thoroughly cleaned out before you put them all back into it, so the original piggies no longer recognise it as their space. It then takes a further two weeks for them to fully establish a relationship. You cant repeatedly introduce and then separate them as that interrupts their process and causes them stress.
Bonding and Interaction: Illustrated social behaviours and bonding dynamics
Dominance Behaviours In Guinea Pigs
