Oops...meant to add...
We keep the entire area mowed well which is why dh hates mowing around those close pines. Can't get the mower between some of them. So if we could grow something that would spread out in a line along the property and only be about 3'wide/deep, so dh could mow directly up to it, we would be in heaven. As for the running bamboo, would it be kept under control just by mowing up to where we wanted it to grow?

What you want to do with bamboo is possible, but here are the things you should know that are drawbacks:

1. Clumping bamboo, by definition, is not going to move much of anywhere. Each clump will get a little bigger each year, but, if you want it to form a hedge, you'll have to get a lot of plants and place them at maybe 4' intervals...and that's going to be more expensive than a wooden fence.

2. Running bamboo will fill in faster, but you'll have to maintain it, and that means rhizome pruning with a sharp shovel once or twice a year to keep it within the boundaries you want. I do this with all my runners and it isn't much work and saves me the trouble of buying and installing bamboo barrier in the ground. The problem I see for you is that you might have a lot of tree roots where you want to plant the bamboo, and that would make rhizome pruning a lot more work.

3. If you plant bamboo for a hedge, plant it in sections with different species. The reason for this is that bamboo occasionally flower at unpredictable intervals. A particular species might flower next year...or not for a hundred years. When it does, it typically means the plants you have weaken or die. Often, if they don't die, it takes years for them to recover. This may never be a problem for you, but you just should know beforehand that relying on only one species for a hedge involves a little risk.

I forgot about your mowing question. That can work, but it doesn't kill the rhizomes in the ground, so they can keep moving out and come up quite a ways away. With rhizome pruning, everything beyond the cut line dies.