Sorry, in my already long post I missed that you asked for rough costs, it's a bit of a how long is a piece of string question and can really vary also area by area but I would say there are a couple of options.
Most basic is a hardy horse kept in the most low cost way at a very basic DIY or grass livery so the point of having a sharer really is to relieve the owner of all stable jobs and responsibilities for some of the week rather than financial. The cost for this will usually be fairly notional, maybe around £50 -£75 a month (or sometimes no financial contribution at all required) but there will be a lot of care jobs to do esp in winter e.g. muck out stable, fetch horse from field/return to field, change rugs, make up haynets and feeds, scrub out and refill water buckets, poo pick and weed field, sweep yard, tidy muck heap, clean tack etc., maybe around a hour or an hour and a half's work a day not including riding time? The cons of this aside from the time required are these kinds of yards can lack the facilities of a more expensive like a floodlit arena and showjumps, in the winter she may struggle to ride in the evenings or may be limited to hacking or riding in the field only which is obviously tricky in the dark after school!
In the middle you'd have your part-livery option, where the owner pays the yard for some or all of the care of the horse, there may still be some jobs required but probably more along the lines of skipping out, changing rugs, grooming, topping up water and hay with perhaps more to do at the weekend, perhaps 30 mins work per share day in the evenings and an hour at weekends, not including riding time? Facilities for riding likely better and there may be yard staff around to lend a hand if she gets stuck although be wary of assuming they'll step into a parental/teaching role. The costs here usually equate to a % of the livery fee relating to how many days the sharer does, around here 5 day livery is around £500 pcm so a share would be in the region of £200 pcm for 2-3 days a week depending on the exact yard and arrangement.
At the top end is full livery where very few jobs are required and it's essentially turn up and ride, some light work required like light grooming, throwing in a ready made feed after riding and so on, but nothing taking significant time. Again usually nicer facilities so you can ride year round, often a good set of showjumps and a choice of different arenas, and if she gets very lucky there may even be an opportunity to go out to outside clinics and competitions if someone else on the yard is going out in their box and willing to take her for diesel money. Around here full livery at a fancy/competitive yard is £750-£1000 pcm so a share would be up to £500 pcm.
But like I say those are very rough costs and I am in the SE so it may be cheaper elsewhere. When doing your sums do factor in the costs of getting her to/from the yard and at least a monthly lesson, if she does want to compete or go on outings that's an expensive endeavour with transport and the kit required and entry fees etc (and finding a share horse she can compete/go off the yard on isn't easy as of course the owner will usually take priority) - again she may not have thought about this now or may swear blind if you allow her a share she'll never ask you for anything ever again (I've had teens!) but if/when she gets onto the yard and makes friends with a bunch of horse-owning friends who are off every weekend for fun rides and pony club and competitions it's totally natural that will be the next thing she's desperate for!