I was a bit worried from your spelling of meter you were in USA, which would take me out of my comfort zone. Your location means that any of the standard bamboos sold in Britain will do well for you.

If you think that being in a border 1.5m wide means you aren't worried about spreading, then you don't know how bamboo can spread! If you have an agressively spreading type of bamboo, you can have a culm coming up 1.5m away from the main clump in just one season. If there is a lawn behind you border, you can mow it out, so that is OK. But I would be worried about what is beyond the ends of the border, and maybe put in a barrier their, especially if it is neighbours or something.

If you want bamboo that is only about 3m high, and very little worry to about spreading, then I would consider the Fargesia family of bamboos. They are true clumping bamboos. (Unlike the "clump-forming bamboo" of garden-centre parlance). They are also relatively cheap, at least the standard types, if you shop about for them - also people selling them at fancy prices to people who don't realise they ought to be cheap. To save money, buy some larger samples, and divide them, and plant at 0.5m intervals, and you'll have your screen in about 3 years if you keep it well watered/fertilised. Best time of year to do this is Sept, but March/April is OK too. Some of them are too small, F. rufa too small, , F murieliae has some smaller forms which may be too small (simba might just do you jumbo would definitely be big enough), but the basic kind is probably just right. F. nitida had a flowering event recently (which kills it), so make sure your seller is selling you post-flowering F. nitida if you choose that - the problem does not exist with the beautiful juizhaigou forms. F. scabrida, a beautiful one, is a bit more of a wild card, turned out to be somewhat spreading for some people, (and may turn out not to be Fargesia - it is difficult separating it from Yushania and Borinda).

The other strictly clumping type that is reasonably hardy is Thamnocalamus. I have a T. crassinodus Merlyn and it has been defoliated by the recent winter, so we learn it is not as strictly hard as Fargesia, but I'm reasonably sure it is still alive.

The Phyllostachys family is the main family contains many beautiful bamboos, but they are spreading. In Britain in many cases they only spread slowly, especially in cooler drier areas, though some are pretty aggressive even here. Also they can take a good decade to establish themselves properly. And how aggressive they are depends upon species and the conditions. If you have a nice warm site with damp soil, as you might in SW London, you could grow some monsters, so be careful with your selection, if you don't want to get much more than 3m. If you are looking for something not too enormous, then the popular black bamboo (P nigra) is usually less agressive, but be aware that some specialist types of P nigra such as henonis are more agressive and not black. P. aurea is also less agressive, but the standard type is a bit boring, and green not golden, there are pretty ones such as koi and holochrysa. P. aureocaulis spectabilis is a lovely one, not too large, but it is a bit more aggressively spreading. You will find others in the breeders' lists.

If you like plain green bamboo, then Semiarundinaria fastuosa is the classic green hedging bamboo, though in good conditions it will grow 5m easily, and can get aggressive.

You will find Pseudosasa japonica widely sold, and will probably grow about 4m or something, and many people say it is not too aggressive - I have one which is proving very nonagressive, but it is in a dry spot. With their persistent culm sheaths, it has a different look which you like or you don't.

Have a look around some of the specialist bamboo-seller websites for descriptions of bamboos, and remember, they always downplay the spreading aggressiveness.
Some good ones are
Jungle Giants | Bamboo Specialists Homepage
Whitelea Nurseries
Pan-Global Plants - Home (not mail order)
Hardy bamboos | grasses, herbaceous, hardy exotics, hardy in the UK, rare bamboo and grasses, buy from hardybamboo.com and PW Plants