does she not fancy enduros herself?
as for cross id say yes budget is enough. don’t think of it like a ‘weekend of racing’ though or you might be disappointed. its more ‘a few hours on a sunday you can fit round the other stuff in your life’. at most its an hours sign on and warm up, hours* race, half an hour cool down/faff/pack up.
british cycling website should have the links to the local league in your area.
I’ve not really sold it there have I? its good fun but i wouldn’t want it to be the only riding i did.
*some leagues lump the women in with juniors and vets so she could only be doing 45-50 mins.