In my dreams! Apparently there are people here who have what locally referred to as "Japanese timber bamboo", but we're waaayyy... warmer than you guys.
My ideal would be giant timber running bamboo, but I'll settle for anything that won't die!
There are some clumping bamboos that are leaf hardy to -20F, but they are shade lovers and are sensitive to heat, so they would not survive due to the direct sun and summer heat. The cold hardy running bamboos are only leaf hardy down to -10F, but their roots are actually tougher and more cold hardy than the roots of the clumping types. These are my recommendations:
Phyllostachys bissetii - This species seems to be the toughest and most cold hardy, and it has foliage branching almost all the way down to the ground.
Phyllostachys aureosulcata and ‘Spectabilis’ variety
Phyllostachys atrovaginata - This species has the strongest wood, but foliage doesn't begin until 5-6' up.
In order to estimate the maximum mature height in your location, I would subtract about 10 feet from the indicated height for each of these. Please note, if you do get more than one species, we do not recommend planting them together. We suggest keeping them separated by rhizome barrier or a pruning trench if they are going in the same area.
For cold climates, I do advise starting with a #5 size if possible. The #5 size (average height 4-6') is $95 per plant for each of the above except for the parvifolia, which is $120 per plant. The #5 size ships for $20 per plant. You could only get a couple of #5 size plants and stay under $250. You are welcome to try them in smaller sizes if you want to experiment, but a #5 has a better chance of making it the first winter.