Yes, they stack.
You touch a quiver containing ammunition. When a target is hit by a
ranged weapon attack using the ammunition, the target takes an extra
1d6 fire damage. The spell ends on a piece of ammunition whether it
hit or misses, and it can only affect up to 12 pieces in total.
At Higher Levels: The number of pieces of ammunition you can affect
with this spell increases by two for each slot level above 3rd.
Conditions to meet:
- Must be ammunition
- Must be in the quiver that is enchanted
- Must hit with a ranged weapon attack using the ammunition
Does the spell include any rules about other bonuses not affecting the item:
Is there any rule precluding the bonuses stacking?
Do you meet these conditions:
- Is a +3 arrow ammunition? (Yes)
- Is the +3 arrow in the quiver when the spell is cast? (assuming yes in your example)
- Did you hit with the ammunition via a ranged attack? (Yes, using a bow is a ranged attack, Yes, I'm assuming you did hit for purpose of the answer)
Therefore, since there is no wording stating the Bows bonus cannot be applied it gains the bow's bonus. Also, since there is no wording stating magical arrow bonuses cannot also be applied it also gains those
So yes, you would gain the +3 from the bow, the +3 from the Arrow and the extra 1d6 fire damage from the spell.
Further, affects like Sharpshooter, Hex or Hunters Mark would also stack, if they apply to your attack, as there is nothing precluding them from doing so in their wording, the items wording or the wording of the spell.
As to SeriousBri's comment:
The spell isn't making the +3 arrow in the example non magical when it hits. The magic item itself becomes non-magical after it hits a target based on the description of the item. It has nothing to do with the spell, so there's no added risk by using the spell.