Where there is a will there is a way and that bush has the will and will find a way. Aside from that glib remark of mine the only recourse I see is to remove the bush. Cutting and removing the roots will only stimulate more to grow. Weed killer will kill the bush but even if it did not that would be only be a temporary measure. Since you talk about a bush that runs alongside the back of the border are you talking about more than one?

A photo would be useful also do you know what the 'bush' or 'buses' are?

Less drastic would be to put a barrier such as a narrow sheet of corrugated iron or even hardwood into the trench, about 18" deep. Obviously metal would last much longer. I have a neighbour who has done this for exactly the same reason and it has been very effective for the last 20 years. Very occasionally a root pokes through or under but is swiftly dealt with. The hedge that was causing the problem is mostly blackthorn and privet.

If its blackthorn it will find a way somehow. I hope for your sake it isn't.

It is expensive these days, but the best way that I know of is to dig a trench 30-70 cm deep, and put in a barrier of copper screen. When young roots touch the screen, the copper kills the growing tips. That may be enough to stop the roots, but sometimes they will grow under the barrier.