I think whether or not they can offer a bursary at a mid-point entry, is whether they have any funds left, or indeed any spaces. If a school is spent to the maximum, one more may be a significant problem. Some wealthy schools may be more flexible. It just depends.
When you go to the open day, see if you can find the Bursar. They should be able to tell you what the financial position is likely to be for an in-year transfer. It may be that you have to wait for Y9 entry, but not necessarily.
If you get a bursary, it is not necessarily financially crippling to afford other things at school. Yes, there will be expensive trips, but not everyone goes on them! Skiing is not part of the national curriculum and is voluntary! Likewise MUN conferences. If a trip is part of the curriculum, schools often offer some help to bursary holders anyway.
If your DD is fed upwith the messing about at her current school, (and they should be stopping it), she deserves better. Write down the questions you would like to ask and, if need be, make a separate appointment to see the Registrar and possibly the Bursar. Go without your daughter so you can have a frank and honest discussion which will allow you to decide what to do and when/if to apply. Hope it goes well.