I did 2 years at uni doing adult nursing. It wasn't for me and I'm no longer doing it, but that's besides the point.
I think it's good that you're doing an access course 1st. I jumped into it straight after school before really knowing that I wanted to do it.
Anyway, sorry, I'm going off topic.
Before I started, I volunteered in a hospice for a summer. If you can get something like that for a longer period, that'd be good experience. You could also look into being a care assistant in a nursing home or somewhere like that. A lot of people on my course had jobs like that and it set them up well for the course.
Like the post above said, it's not easy to get relevant work experience, especially in such a short time. Try your best to get something, however, I was accepted into uni before I even did my hospice volunteering. Just show a keenness for the course and you should be fine.
Good luck! If it's what you really want to do, you'll be great at it.