Firstly, I'm wondering what hedging or fencing exists between you and your neighbour at the moment, and whether it might be simplest to beef that up.
In my opinion, your bamboo screening idea would work.
It's possible to grow very large bamboos in very small pots. Here's a young Phylostachys growing in a pot in my own garden...
That plant will grow much bigger, and would grow satisfactorily in a much smaller pot than that one. Garden centres will have tall bamboos for sale, to take away, in very small pots. The main problem about growing a bamboo in a small pot is that they can topple over.
The photo above illustrates the main problem you'll have... Most bamboos have a habit that is described as 'graceful'. That means that when it rains, the plant effectively flops. So if you plant this alongside a path you'll get wet when you walk past.
There are a few bamboos that do not flop. Suppliers describe these as 'erect' or 'bolt upright'.
So you'd need a bamboo that is clump-forming (not invasive), and evergreen, and erect, and of a suitable height for your purposes. I'm sure a specialist supplier could advise you of a suitable variety.
You might also consider plants such as Arundo donax (Spanish reed). It's very tall and very upright, and will grow in a pot, though it's not evergreen. Or some tall erect varieties of Miscanthus, which are very similar.