I just bought some small Blushing Bride. The branches are about 6-10” Will they bloom this year?

You should see blooms this year! Have you planted it in the ground? Be sure to keep it well watered as it establishes and the soil evenly moist throughout the summer. The pot should have fertilizer in it already so you won’t have to add more this spring, but in future months that will help. Here are some other suggestions for maximizing your blooms this year and beyond: https://youtu.be/mkuyY2-UfDI.