Cost of education should definitely be part of the decision process and so should the length of the program. Students pursuing masters level degrees have more opportunities for financial aid via fellowships/scholarships/lower rate loans, than you would have pursuing a 2nd Bachelors degree. And adding an extra year of school will end up costing anywhere from $20k -$40k extra depending on the school and your living expenses. Additionally, as you get further into your twenties and thirties, adding that extra year on to an education program starts to become a much more serious commitment than it was in your early twenties. These are big decisions, so I just hope that the OP (and others in their situation) takes all of the comments here with a grain of salt and does what appears to be best for him/her personally in their current life situation.
That said, I have an bachelors in Mechanical Engineering and did a 2 year Masters in ID Program. I currently work as an ME/ID hybrid at a small engineering firm. I came in as the 2nd class of a newly started program, and was not required to do any preliminary fundamental classwork. I will honestly say that I wish I had been required to take those fundamental classes (art history, color theory, etc). And I definitely wonder at times if doing a Bachelors in ID would have been a better choice for my professional development and would have allowed me to transition completely into ID.
However, with respect to finances and life-planning, however, I am completely satisfied with my choices. I got to spend 2 years as a full time grad student, graduated with a relatively low amount of debt thanks to a fellowship (which I wouldn't have had access to pursuing a BA), and found a job at a good company in a new city paying me more than I was making prior to grad school.
As many threads on this forum will reiterate, no one cares about your transcript or GPA when applying for jobs. Only your portfolio matters. I believe it is hypocritical for people to say that, and then scoff at others who take the masters route because they feel like it is "cheating" or something. The reality is that everyone applying to a job posting with the position of "Industrial Designer" will be judged by their portfolio and essentially has the same chances of getting that job with their entry. (spoiler: chances are low, but that is a topic for a different thread). Whether you get there by adding an extra year of structured school study, or fitting in additional self-study of the fundamentals during a compressed schooling program, you'll end up with new skills and experiences that will shape your professional career and your life. So, either way... you win!