I've suffered from CTS for over ten years and have been able to manage the pain to move forward without surgery.
1) Understand that the pain is your body's way of telling you something is wrong. Don't play through it. STOP and rest.
2) Read The Bassist's Guide to Injury Management by Dr. Randall Kertz. He is both a bassist and chiropractor/acupuncturist. This book will give you additional understanding of what's going on in there. You can buy it here: http://www.drkertz.com/buy_book.html
3) I've found that it was more than bass playing that caused me pain. Spending so much time working on laptops was a portion of it, as well as my posture. Find other things in your life to correct.
4) RICE Method. Rest when you're in pain. Ice the affected area. Compression. Elevation. DON'T KEEP PLAYING!
5) I am able to manage living my life with bad CTS in my right wrist by doing all of this. A little bit of Tylenol and REST will go a long way.
Yes, splints help. If I'm feeling achy in the wrist, I will use a splint at night. But right around this time every year, from being cooped up indoors and spending more time sitting still, with poor posture, and a laptop nearby, I end up putting myself on rest for about two weeks, in the splint with minimal usage.