If you aren’t incapacitated, you can add your shield’s AC bonus to any Dexterity saving throw you make against a spell or other harmful effect that targets only you.
Yes, it does
No distinction is made between the normal bonus to AC and the bonus as a result of the magic item. They are simply bonuses to AC. Since both are part of your "shield's AC bonus", they are both included.
A shield is made from wood or metal and is carried in one hand. Wielding a shield increases your Armor Class by 2.
While holding this shield, you have a +1 bonus to AC. This bonus is in addition to the shield's normal bonus to AC.
Notice that neither of these bonuses are made distinct by a title like "shield bonus". They are just bonuses to AC that come from the shield.
The +1 is part of the shield's AC bonus for this purpose
Unlike in previous editions of D&D, 5e has very simplified shield rules:
Wielding a shield increases your Armor Class by 2.
Naturally, some shields are special; the +1 shield mentioned increases your AC by 3 instead. However, if "special" shields that give different AC bonuses aren't intended to affect the benefit of Shield Master, then Shield Master could simply be worded as "add 2" rather than "add your shield's AC bonus". Since the wording of the feat implies that some shields give a different bonus, and magic shields are the most common reason I know of that a shield would give a different bonus, I conclude that the different bonus from a magic shield is intended to apply.