They will remain bush beans. Beans ( P. vulgaris) are self pollinating, so saved seed is normally true.

I highly recommend collecting bean seeds from this year to plant next year. It couldn't be easier. But if it's a hybrid and not an open pollinated variety, then the seeds won't grow into the same variety next year. All the beans I've ever planted have been open pollinated. I'm not sure what hybrid varieties if any are out there.
And you don't have to worry about cross pollination since the flowers usually self-pollinate even before opening.