Hi! Great that you want to get your own girl a friend! How old are the piggies in question?
Guinea pigs can have very pronounced likes and dislikes, which is surprising for a species that is so needy of company! You will often encounter a good measure of wariness and fear in guinea pigs that have been living on their own for some time, which can more easily manifest in rather aggressive behaviours during the initial meetings.
Give any piggies that you cannot date/meet&greet before bringing them home several days' time next to each other to get used to their new home and their future friends; that will help to minimise any additional stress factors before that introduction on neutral ground proper and thoroughly clean/neutralise/rearrange a cage Including walls and any fittings) before putting a newly bonded pair in. Always remove any hideys and corners where one piggy can get cornered; that is the place where fights/scratches and bite can suddenly flash up simply because a piggy feels trapped or can't get our of the way quick enough. Make sure that both piggies have their own hideys and food bowls, even if it is just hankies pegged to bars at the beginning in order to prevent any trapping.
If you are rehoming from an uncertain background or a place where your new piggy has not already undergone a mandatory quarantine, we additionally recommend a quarantine of at least 2 weeks away from your own piggy to make sure that nothing infectious like mites, fungal or URI (respiratory infection) is carried over. If necessary, have her checked over by a good vet.
But even if they don't get on immediately, two single piggies will still be much happier with a next door neighbour of their own kind they can interact with all the time. With a bit of patience and persistence, many sows will come round. Unlike with boars, you can do an intro over several days with sows, but you still need to do it in longer stretches of time for bonding to happen and you will still need to tolerate all mild and medium aggressive dominance behaviours; 5 minute meetings will get you nowhere and even with an hour together daily, they will seriously struggle to work through the bonding protocol. Only separate if there is serious tension or aggression that could escalate into a full blown fight and abort the bonding if there is a fight because after one piggies will usually not go together again. You are OK as long as the girls are working in the "maybe us" zone, but once they have decided that a piggy is "not us", you've had it.
Guinea pigs need to establish a hierarchy in order to work as a group or a pair. Unlike you, guinea pigs know the manual for bonding; what looks to us like bullying is actual acceptable behaviour and an integral part of the bonding process. The submissive piggy will often scream loudly, not in pain but in submission. Any nipping and head butting is not really all that painful, it is a way of demonstrating power for the topt piggy - things usually look a lot worse than they actually are. The dominance phase, which always follows the initial short acceptance phase can last anything from a few days to a few weeks.
You may find these threads here helpful:
http://www.theguineapigforum.co.uk/threads/sow-behaviour.38561/
http://www.theguineapigforum.co.uk/threads/faq-introducing-and-reintroducing-guinea-pigs.38562/
http://www.theguineapigforum.co.uk/threads/dominance-behaviours-in-guinea-pigs.28949/
