Bees or hornets bright orange in color?

There are many varieties of bees...

I suspect what you are seeing is something much like a bee, (order Hymenoptera), but somehow didn't match up to your eye's common pattern matching of a bee. This may be the case if you are looking at a bee mimic insect such as a Bumblebee Robber Fly, (Laphria flavicollis). If so this is a remarkable and beneficial creature to orchardists! They are hunter-killers of damaging insects in fruit orchards and gardens. They are one of a very few species that have been known to devastate large numbers of Japanese beetles. This among the robber flies is one worth breeding in captivity and releasing. Note and warning. This fly is not specific about its prey and can also wipe out large numbers of honey bees so we must be observant of local aviaries and be a responsible steward of these beneficial insects.

There are hundreds of other varieties of bees native to North America. They come in various sizes and colors.

You could also be looking at a mason bee which is black and is a very efficient

pollinator, hard worker and will fly in weather that a honey bee won't.