well first off, you need to decide if you can manage to pursue a PhD without any financial aid. I wouldn't really advise that route.
There is the possibility that scholarship positions will open at her Uni in the next year, so waiting for that is a possibility. Or there are, in most European Countries, government funded scholarships available. These are very competitive, but for most, you don't need to be registered as PhD student to apply, but you do need to have potential supervisor on board..You could ask if she is aware ( and she should be) of any of these types of scholarship and if she is willing to work on an application with you.
Apart from funding, other things to consider are what resources, lab equipment, samples, funding available for research expenses. And if there is the opportunity to teach available.
Also if there is finding for attending conferences.
Other things to suss out, with out directly asking (maybe by looking at their online profile) is how many PhD students they have supervised to completion. I would read some of their articles to get a sense of both the standard of their work and also if it is a good fit for you.
I would also see what training is available, so depending on your research it could stats training or qualitative research training ect. and the availability and funding of these types of thing.
other than that I can't think of anything else to ask.