Lonicera sempervirens, the native trumpet honeysuckle. I have 'Major Wheeler' which the hummingbirds like and which blooms from May until freeze. Depending on the pergola's structure, it (and many other vines) will need help climbing the posts.

Thank you for the suggestion! I've done a little research on it and it seems like it's going to be perfect!

Since you are in Denver, you might want to take a field trip to the Denver Botanic Garden to see what if anything else they have that would work. I have memories of structures with vines there, but no specifics. It's worth a visit regardless!