I may be wrong, but I believe the accelerated BSN program you mention is likely to be designed for people who do not have any sort of BS/BA degree, yet have hands on experience in patient care. You on the other hand have the advantage of already completing a BS program in another discipline, therefore you already have completed a core curriculum. I would look at BSN programs, compare the prerequisites they require with the coursework you already have, consult with their admissions counselor about any gaps you need to fill (hopefully not many) and then apply directly to BSN programs. Remember, the first 2 years of most 4 year degrees are spent on core coursework. You may well be able to complete a BSN in little more time than an ASN degree would take, yet you would greatly benefit from the higher level BSN degree over the course of your career.
Should you find that you still need to look at the ASN degree, I believe there are no worries about finding a job providing direct patient care. I believe the ASN degree will only hold you back if you are interested in further pursuing advanced care programs (like becoming a Certified Nurse Anesthetist, Certified Nurse Practitioner, Certified Nurse Midwife, etc...) or are interested in a management track career.
Good luck to you on your educational pursuits, whatever they turn out to be!