Bamboo

Bamboo can be difficult to control, if it's the running type the roots are very invasive - the hebe is likely to be smothered by it.

I am forever getting rid of new bits that have popped up. Even in the lawn! And then I get a whole bare channel in the lawn where the root was. It's not great. I hope the hebe will be ok.

If I were you I'd move the hebe to a sunny well drained spot & I'd hoick that bamboo out - sounds like it's the running type.

The hebe is in a good spot, plus I have hardly any room left in my little garden already. I cut the bamboo back a lot to make sure it wasn't shading the hebe and I will keep an eye on it. Yes, considering "hoiking" it out but not sure at the moment. Funny how it seems to want to come up in the lawn but not so much to the sides of where it is in the border. I wonder if I put some kind of wall in the ground around the roots if that would contain it? Sort of like having it in a tub but without having to uproot it to do it. Or else hoik it out yes but then start it off again but in a large tub so it couldn't destroy the rest of the garden.

Bamboo roots are very strong, a pot won't contain it, I'm afraid. It's even known to grow through retaining walls.
It will come up on your neighbours side if it hasn't already. It spreads via rhizomes, so it will keep coming up in your lawn unless you dig them out.
You could try growing some in a tub on a patio if you want to keep it.

Yes I will quite likely try that. Not sure how I will be able to get it all out of the border though except maybe if I get a big tub going on the patio first then literally kill the one in the border off with some weedkiller on the leaves that will go down to the roots. I used some on nettles in my previous place and it worked well. The nettles had that kind of roots going quite a way underground and very thick. They took me ages to dig them out!