I usually use King Arthur flour, and I beleive that its AP has a higher percentage of protein than many other APs, so if you are using a brand like that you might be splitting the difference. (Other brands might be more variable). Unless you were making something like bagels (which ideally use extra-high gluten flour--think about how chewy they are!) you should be fine. Some bread recipes (like for french bread) prefer that you use AP in fact.

For a soft, "sandwich" type loaf (baked in a loaf pan), I'd use unbleached all purpose. Bleaching adds chemicals you don't want/need. For an "artisan" crusty loaf, or pizza crust, where you want a sturdier crumb, and heartier bread, I'd used unbleached bread flour, since it has higher gluten, and will give you a stronger bread.

I use mostly bread flour for my challah (egg bread) with a small percentage of AP flour for delicacy. You'll get a nice stretchy crumb with bread flour; but using 100% AP flour you'll get a shorter, more breakable texture, not as nice for bread i my opinion.

There's no difference between the protein count in AP flour, be it bleached or unbleached. Unbleached flour simply means that it hasn't been commercially bleached; therefore, its color is more like ivory. White flour, however, bleaches on its own after a period of time. That is, it will lighten in color as it ages.

There IS a difference in protein amount between AP and bread flour, however. The higher the percentage of protein, the more gluten development, which is what you need for the best bread (although AP is just fine).

Use bread flour if you can....I'm a convert after so many failed attempts with AP flour. I'm finally getting my bread almost right.

This answer comes from Shirely O. Corriher, Cookwise, page 4 - 7. I will just share the bottom lines. You can use all purpose flour if it is unbleached. Bleached all purpose flour has too little protein for outstanding yeast breads.

Unbleached all purpose flour works for yeast breads.

And bread flour has the most protein and works best for yeast breads.