In his [url="http://www.amazon.co.uk/Todd-Phillips-Essential-Techniques-Acoustic/dp/B00024OR4Y/ref=sr_1_3?s=dvd&ie=UTF8&qid=1297423565&sr=1-3"]Essential Techniques For Acoustic Bass[/url] DVD, Todd Phillips recomends, as an exercise, trying to finger the notes without the thumb pressing on the back of the neck. This is to help build a technique where you are not dependent on the hand grabbing the neck.
I have argued the point of keeping your elbow up with Jake before. My elbow sits relatively low but my wrist is still straight. I guess I have the bass tilted back slightly to allow this. I used to keep my arm up but that led to shoulder problems. With my arm down now there are no problems whatsoever. You just have to experiment to find the way that suits you. And yes get a teacher, says he who hasn't done that.