Here is some information to ponder:
If you complete an undergraduate degree in Health Sciences and then pursue an accelerated degree, you will lose grants such as the Pell Grant (if you're receiving one). The only other method to pay for school is either out of pocket or with student loans. Also, you will be in school for an additional one to two years.
There are tons of RN to BSN programs, many online. One advantage is that you could work as a nurse while completing your BSN. Furthermore, many facilities will contribute to paying some of all of your tuition. This may be the quickest route to a BSN depending upon which school you attend. The courses you have taken will be applied to general course requirements.
The traditional BSN route would be wrapped up and completed for when you start your career. This would not be the quickest route as traditional degree program will take you five years to complete.
Ultimately it is up to you. If I had it all to do again, I would have completed the ASN and had a facility pay for my BSN. Instead, I went the accelerated BSN route and paid a mint for the degree.