Any player can develop the habit of "shoulders up" into their playing.
All this means is you are lifting your shoulders. This can happen with ease to any player if they are not aware of the signs that they are doing it. Normally they are tension and a 'warm tired' ache in the shoulder are we call the rotor cuff.
To feel what a relaxed shoulder down position is do this.
It is called neck shrugs and as it sounds you just life both shoulders as if you are shrugging them. But what I want you to do is exaggerate this movement...really lift them so you neck goes deep on to them, then drop the shoulders pulling them back and pushing them down as far as you can go....the natural rotation will will bring them forward again to a neutral position when you relax.
Repeat this at a moderate pace about 10 times, then on the last one when you push down just relax and fell that position.
This is the normal playing position, your shoulders should never lift when you play. Do it in front of a mirror, use it as a warm up and warm down, so before and after playing. Use it when ever your neck or shoulders feel tired.
As a new players you will use your neck to look over the bass at your hands, so you lift your shoulders to do so, because you need a visual reference of what you are doing. The problem starts because you look and play at the same time, so your shoulders do not go back to being relaxed.
Common problem if you read music as well, you push your head forward to read and play, rather than remember to bring the stand closer so you can stay relaxed and play. But sometimes this is not always possible because of space, so the habit can develop.
If you stand and play it is easy to favour one side, so again make sure you weight is even, your hips level and your spine relaxed and straight...even when sitting.
Remember the shoulders do not hold up any arm soley, it is a combined use of the upper body muscles that give you the correct relaxed posture.
That posture for the want of a better word is down.
If your shoulders are down they are relaxed...you have to introduce muscular tension to lift them.
It is this unused tension that will create problems because it is extra tension that is not needed so it is sustained tension. Because your focus is in playing it is not always noticeable during playing, but usually afterwards when you try and relax them and they do not.
The shoulder shrugs will remind you of what keeping them down and relaxed is about.
Here is a link to some basic hand exercises, I am shooting some new videos later this month and one of them will deal with posture and will have the routine I use everyday for my warm up/down. It is a combination of stretches and muscle glides that I use in an easy couple of minutes routine, but here is the hand and arm part. http://www.youtube.com/watch?v=C_FZichHw1w&sns=em