My wife is Masters Level, CCRN who has over 25 years of critical care and management experience. She states that, in the very near future, the BSN is going to be viewed as the standard for nursing. There are so many RN to BSN programs out there, and a lot of them feature most of the work being done online in a distance learning environment.
I don't know that you absolutely need to have ICU experience for CRNA school, as I know a CRNA who went from a BSN program to CRNA without ICU experience and had no problems at all. Just do some research.