Yes, you can pursue an advanced degree part-time, though keep in mind that there often is a deadline to get it done (e.g., in my state, you've got six years to complete a master's once the clock starts ticking). It's also possible to get an extension if you find yourself in a bind. For me, an accelerated BSN was affordable; now that I'm working full-time, the hospital will pay for my master's, which I am working on on a part-time basis.
Something else to consider: Do the hospitals in your area prefer BSNs? This is a growing trend. In Boston, for example, the BSN is the preferred degree, and many posters on this board say it's tough to get a job in a city hospital with an ASN. That's certainly not the case everywhere. But it's worth looking at the institutions where you might want to work to find out what their current requirements are before you decide which degree to pursue. (In my area, city hospitals prefer BSNs for ICU jobs, for example, but the trend is toward hospitals here to seek magnet accreditation, which means if they get it, they commit to promoting only BSNs, not ASNs. Something else to consider if you want to keep your options open.)
An accelerated BSN takes about 15 months, give or take, depending on the program, and it goes year-round. (So do some ASN programs; in my area, the drawback was that they were only offered on spring-fall semesters, which meant a three-year commitment including pre-reqs. That was far too long for me to be out of the job market.) You can do many of the pre-reqs online and take advantage of community college prices (around here, $80 a credit hour), then transfer those to the accelerated BSN program. Always a good idea to check with your target nursing school first, of course, to make sure they'll accept the credits. The accelerated BSN is intense -- about 500-600 pages of science reading a week in my program -- but given that you've already done a JD, you'd likely find it quite manageable.
One other thing to consider: Where do you want to work? My adviser urged me to go in at the highest academic level I could, and initially my target was a master's degree for non-nurses. I'd have come out of it as a nurse practitioner. But once I was sure I wanted to work in a hospital setting, she urged me to go for the BSN because it would be difficult for me to find work as an NP in a hospital with no experience. By going for the BSN and gradually earning a master's, I preserve my income, get the experience and let the hospital pay for the higher degree. Ka-ching!
I saved up for a long time to go back to school, and I took a substantial pay cut to become a nurse. Am I happy? You bet. Who cares if you're 39? You'll be 43 in a few years anyway, whether you're a prosecutor or a nurse. If anything, you bring life experience to the job -- and that's invaluable in stressful situations. And consider this, as my adviser once said to me: You don't like your current nursing job? Reinvent yourself. Find something new. Nursing has so many, many avenues to explore.