The spread of the bamboo will not be affected by those other plants. In fact the plants will get somewhat squeezed by the bamboo over time, but there is no need to dig them out, and it may look nice that way.

One other thing: S. fastuosa is a great selection for a hedge as it is so bushy and vertical, but it can be a pretty aggressive runner, so make sure you are ready to rhizome prune regularly in a couple of years if you haven't put in bamboo barrier.

Kudzu I have not put down a barrier, I have it planted against a chain link fence bordering my neighbor. My neighbor cuts his grass regularly.

I know everyone says barrier or rhizome pruning, but how can bamboo survive a riding lawn mower once a week? Am I setting myself up for trouble?

I want it as close the the chain link fence as possible so that does not leave me a lot of room to get in between it and the fence for rhizome pruning.

joefalco-
The shoots won't survive the mowing...however, the rhizomes will, and they will spread further and further into the lawn at some point. It's possible that some of them will surface and run parallel to the grass surface, but they will not be cut by the mower because they are tough and will be low. They may also travel quite a distance until they bump into something like the side of the house, and then you could have a culm coming up where a mower doesn't reach. All of this is a worst case scenario, and won't happen immediately. Nonetheless, there will probably be a point in a number of years where the spread of the rhizomes becomes a problem. If it were me, and I didn't want to install barrier, I'd have left a couple of feet between the bamboo and the fence to allow rhizome pruning with a pickax on my own property. (A future neighbor may be less accommodating than your present one.)

Rhizomes going into the neighbors yard will cause problems, sooner or later. Probably sooner.
If that neighbor is mowing just once a week, that's plenty of time for a whole bunch of new rhizomes to rise a foot or two into the air. Neighbor will definitely notice.
It's also possible that some groups of small shoots/branches will sprout from the cut rhizomes and leaf out. Mowing these will be replaced by more in a never-ending cycle.
It's also possible that rhizomes in the neighbors lawn will in some areas grow along the surface, degrading the condition and appearance of the lawn.

Rhizome pruning along the property line is highly recommended.

Trouble just waiting to happen.

Dig it up. Replant it, this time in an impermeable barrier. Pour a concrete "planter" at least 18 inches deep, extending 6" above ground level. Pour it all at once, not in sections.

Or buy bamboo barrier.

It's beautiful, isn't it!