I would second what duchesse says about 1:1 time, and also what other posters said about finding her an out of school group or club to join. The more variety in her social groups, the less prone she will be to the effects of bullying, because she will always have another group to turn to if one goes pear-shaped.
It won't take her long to catch up with core subjects if you give her an hour or so a day with the Letts books at the kitchen table when things are relatively quiet. There is also an online secondary school you can book into which gives a full educational experience - I will try to find out a link.
Can I also say that while TVs in bedrooms give privacy, they can also make teens isolated and a bit grumpy, so one clever way around this is to take up some popcorn and both sit on the bed and watch makeover shows or whatever together. Insist it's turned off at bedtime and monitor for sneaky viewing after hours.
In terms of bedtime you are probably aiming for between 9-10 pm with a bit of a lie-in on a Saturday and/or Sunday morning.
Girls of this age often like going off for little shopping and cinema trips with their mates into town, with parents providing a taxi service or bus fares. If you give a curfew and then massive praise for keeping to it, you will prevent boundary pushing in this respect later on. Our rule here is they can do more or less what they like within reason, as long as they are absolutely honest about where they are, who they are with, and what time we should expect them back, so we can send the cavalry out if help seems to be required.
iPods/MP3 players can be important as a means of building a kind of teenage group identity through shared music, so this would be a good birthday present if she doesn't already have one, otherwise be fairly generous on the iTunes budget. These gadgets do get pinched quite frequently though, so don't spend a fortune on it.
Finally, as well as girlie shopping, cooking and baking nice things together is a great bonding experience and allows time and space for chatting things through. It is possible to do this fairly easily even with younger children around.
I think it is just great you asking for advice like this, and I hope you manage to build the happy relationship you obviously deserve!!