Some thoughts on why this thing is so cheap.
1. Shield is not dependent on caster level to be effective. Since it is continuous, even duration is no longer a consideration.
2. The spell is ordinarily Personal, which restricts would could have it and how often, under most circumstances.
Let us analyze what happens if you forbid the combination:
1. Most likely, the creator will simply create a daily item instead.
It is possible to price it according to the bonus. However, "other bonus" is not the way to go. The idea is that deflection is the default bonus, but others are possible. However, armor bonuses already have their own structure, which bracers of armor follow. Priced as a +4 enhancement bonus to (no) shield bonus, it would be 16,000. That's without the immunity to magic missiles effect, which is probably worth less than 2000. So let's call it 18,000, under the assumption it is an amulet, cloak, bracer or other appropriate device.
The proposed item has one major flaw:
1. It's caster level 1, which means any dispel magic is going to knock it out for 1d4 rounds.
Now, bracers of armor +4 require caster level 4. They are based on mage armor and have a caster level of 7 or higher. Now, bracers of armor, if they simply had mage armor as a continuous effect, would cost 1000 gp according to the price scheme in the origional post. Mage armor is conveniently also a 1st level effect; it can be cast on others, but OTOH has a longer duration. Even a 7th level mage armor would cost only 7000 gp, rather than 16. This is similar to permanent spells and various items having a higher requirement than the base spell.
So, at the very least, the proposed item should require a higher caster level, probably 8 (twice the shield bonus, as bracers of armor are to mage armor). That raises the price to 32,000 gp, which is actually higher than the above price.
Thus, if I were the GM, I would say you have two options:
1. A continuous shield effect with caster level eight, for 32,000 gp, which includes immunity to magic missiles, or
2. A +4 shield bonus to AC item, based on force, for 16,000 gp, with a minimum caster level of 8 (7th, or as in this case, twice the bonus).