Red osier dogwood is common to the swamps of new jersey,and as a shrub prone to growing in large clonal groups,it would love to have you break off a peice to take home to replant.Find local stock out in the wilds of your area.That way you will know its native,has local vigor,and is not the asian variety.Take a walk on the wild side.
Don't worry about barerooting it, its indestructable

I agree with nywoodsman that you should try to find a local variety. Although I bet the Indiana plant would grow in your yard, you'd be introducing Indiana genes into the local red osier dogwood gene pool. This might be an insignificant thing if done once, and it might not be very significant for red osier dogwood, but if native plant gardeners like us keep moving plants around the country we surely will eventually cause damage to the genetic makeup of native plants. There are plants like red osier dogwood that grow everywhere from eastern Canada to Texas and there must be genetic variation within the species. By moving plants around, we are messing up that natural genetic diversity.

Hope you don't think I'm beating up on you - just trying to point out a potential problem that I think native plant gardeners should be aware of. to propagate red osier dogwood I'ld first try placing a few 1 foot long cuttings with no or only a few leaves on them directly into the ground where you want the plant to grow and keep them moist. Push about half the cutting into the ground and leave the rst sticking out. This could also be done in a pot. I think they will root easily. If not, as nywoodsman said, there should be lots of rooted "suckers" alongside any large plant you find in the wild. One of these could be removed with a few roots and should transplant successfully.

Can red osier grow in east TX.?

It doesn't occur naturally in TX. Might not get cold enough in the winter.