I am assuming its like a gazebo with a deck and closed off roofing with open sides.
As Jay stated, you may move or have other things happen to you before Bob can come out. I am still waiting of a fence he is supposed to help me with. I just went ahead and built it.
Anyway, depending on the size, you should be able to have the deck built, labor and material for about $8 a square foot, using Treated wood. The gazebo or covering, depending on how ornate could be the money demander. You could just have a plain old arbor for a roof and be happy with that. On an arbor your looking at about $6 a square foot using treated wood.
More exotic wood will raise the square footage price considerably. Treated wood runs about $3.50 a square, then redwood runs about $8 a square foot.
Just go to your local fence company and ask about this construction. Most all fence companies retain or have within their employ a deck builder. a deck builder should also be able to build the arbor.
Remember, arbors are for shade and do not shed water. Trumpet vines and the such add to this natural roof of the arbors. Roofs that shed water are more expensive and with high winds they are gone in most cases.
Get some pictures or sketches ready and present them to the builder.