Although most of the hardy bamboos are runners, there are also quite a few hardy examples of true clumping species that won't wander off. And you are in luck because quite a lot of them are fond of (reasonably) shady positions. Check out bamboos from the Fargesia and Thamnocalamus and Borinda families. Fargesia is probably your best bet, they are very hardy. Though if you give it a bit of protection from cold winds when young, some of the Thamnocalamuses may be hardy enough, and some are really nice, look out for T crassinodus "Kew Beauty". But there also a quite a lot of really nice Fargesias, look out especially for F juizhaigou and F scabrida. F murieliae is a useful species, since it comes in varieties of different sizes. The Borindas are quite big and a bit marginal, though tree ferns can be grown in suitable locations in Edinburgh so you may have a chance.

In British conditions, especially areas like yours, quite a few of the Phyllostachys family don't wander very much at all. Though this is not uniformly true, some are quite aggressive. You need to research this carefully, since many sellers will deny that this could be possible. It doesn't help that gardening programmes on the BBC regularly refer to the whole Phyllostachys family as "clumpers", which just isn't true. As it happens, P aurea (golden bamboo) is one of the best behaved, though you will have to choose an uncommon variety like Holochrysa or Koi to actually get golden culms. P aureosulcata has lots of lovely varieties - spectabilis, aureocaulis, Harbin inversa, etc, and they grow very well in E Scotland, but they are more wandering. True P nigra from a good provenance is generally very well-behaved, though varieties such as henon and boryana are not (and they aren't black either). But the P's mostly need sunshine to thrive and bring out their culm colours, so perhaps not so suitable for your precise conditions.

You do have to go to specialist suppliers to get nice bamboos, and they are not necessarily more expensive that way, indeed they can be cheaper.