Let me throw my hat of personal experience in here. I had back surgery in 1993 for a ruptured disc (almost certainly NOT what you have). I have Crohn's Disease, which causes inflammation to show up around my body from time to time. A few years ago, I was having a lot of back and shoulder pain associated with playing and I got all of this same advice. There are a lot of people treating back pain in their own way. You're either going to have to pick someone to listen to, try everything for yourself or start really looking for some causes.
I'll give you my OPINIONS ONLY of the result of my own exploration. I don't claim to actually know anything and your pain and cause may have nothing to do with my pain and cause. (how's that for a disclaimer?).
"Core Strengthening" is the rage right now. Every single thing that you look at anywhere, focus's on core strengthening. "If you're back hurts, it's because your core is weak". It may be true or it may not be true, but it smells like a fad right now to me. There's one every decade (remember how bad for us carbs were in the 1990s?) I suspect that there is some truth to it, but it's not quite what people have bought into right now. Exercise is good, getting strong is good, I don't think any harm will come from doing pilates or P90x or whatever, but I personally fail to accept the "core" is the answer to every medical question as is currently suggested.
Swimming. I think this is the perfect exercise if you are a good swimmer or can become one and have access to a not-overly-crowded pool. I love swimming and know that I would be better off if I could do it every day, but it's not practical for me, here in Seattle unfortunately. I get some laps in now and again when I can. You know if it is an option for you or not.
Chiropractic. - Not for me. Some people swear by it. I suspect that there are some good chiropractors, but it's a big, fast, not-especially regulated industry with a great lobby group that has kept them from the type of professional scrutiny that most MDs go through. Flame me for that if you will, I can back those claims up, but would rather not. As I said, I know people who have good Chiropractors and swear by the results, it might work out for you. I would have no idea how to pick the good, honest chiropractor out of the field. If it interests you, try to find a personal referral and ask that person how long they've been going to them and if they've gotten better of it's just a dependency that they have now. You mind find a good story that you can apply to yourself.
Acupuncture - no one's brought this up, but someone will. People love it or dis-believe. I haven't tried it, most people I know say that it made them better for a little while, but eventually they had to deal with their problems. It is a system based some concepts of Eastern Medicine that I can't really personally buy into; chi, meridian lines, etc. But, I haven't tried it and I'm not knocking it. It's not likely to do any harm.
Doctors - My experience. Your PCP/Family Doc can give you pills, muscle relaxers or narcotics. Maybe that will help, depending on what is wrong. They will suggest exercises, maybe the McKinzie book (Heal Your Own Back). XRays usually aren't helpful because most of the time it's a soft tissue problem that won't show up on a classic XRay. MRIs or CT scans are more telling, but do you need them? Depends on what's happening. Specialists can inject cortizone, which help with pain if it's caused by a specific type of inflammation. They can do surgery if it's appropriate for you. General pain after playing, isn't the type of pain that lead to my surgery, though. You'd need to talk with a medical professional about your specific symptoms. Neurologists, Neuro Surgeons, Orthopedic Surgeons, Sports Medicine or Rehab docs are all possibilities. Not all surgeons are quick to surgery, some are. No matter who you go to, you're dealing with a human being and some are going to be better than others at figuring out how to help you.
Jumping around with your bass in the orchestra pit like Flea from The Red Hot Chili Peppers. Yeah, that's guy's right, don't do that.
Bass technique. For me, I was concerned that this might be a cause. Certainly what we do is very repetitive and I felt like the repetition was causing or aggravating my problems (which I still have to a MUCH lesser degree). Looking at your profile, you'll have access to the right people to assess if there is a technical issue or adjustment to be made. I've made some small adjustments and I'll make more gradually. We all do, right?
Alexander Technique - Don referred me to the best person in my area and I did it for about 6 months. I loved it. I felt great during and after and developed an awareness of myself, structurally and in movement that has helped me in just about every way that I can think of. It helped my playing. Physically, I felt great. It did not cure me or even really get to the cause of my problem. Alexanderists may say that it would have if I had stuck with it for a few years and sometimes they may be right, but I think in my case there was a cause of my worst pain that needed something else. (irrelavant to you) I think Alexander could be the solution for you, depending on cause, but not regardless of cause (I hope that's fair, Don). My teacher was clear that it wasn't physical therapy, wasn't treatment and they don't use words like "cure". It is hard to talk about, which makes it difficult to approach without a huge leap of faith. I neither wish to talk you into or out of it. I really liked it, if I had unlimited amounts of time and money, I'd do it every day. Get a referral from Don and check it out if you're interested, but if you've got a medical problem, I would see a doctor too. Make sure to see someone good. There are some lessor providers here. It's so simple, its very complicated.
Massage - Certainly not a cure, if you find a good masseuse, it's quite pleasant. Again, with unlimited resources, I'd start and end every day with a 1 hour massage. But, it wouldn't have "fixed me" and probably won't with you either, unless you're just a little tense.
Physical Therapy - Helps some people. I've been to good and less good physical therapists. I have a good one now who is my go-to when I need help. She's actually all about the core too, which bugs me a bit, but she's great. Also not a cure.
I'm sorry to say, you're going to have to find what works for you. If your pain is bad enough or interfering enough, you'll have to do it and probably the solution won't be the first thing you try. But, it's worth it, once you feel better and can play the instrument you love without associating the experience with pain.
Again, take it for what's it's worth. My opinions based on my own research and experience. I'm sure I offended someone, it's not my intention. I'm just trying to say that there isn't one answer or one cause. No one credible on a forum can tell you what is wrong with you or how to fix it. Gather up all of our opinions and then proceed locally.