In the spring our gardener friend weeded one huge border as best possible and then we had it covered with a layer of bark to a depth of 3 - 4 inches. A few weeds started to come through but we have used a spot weeder with a collar round the spray to ensure it only hits the weeds aimed at. It has been amazingly effective although fairly expensive to do it properly to the required depth with good quality bark which we bought in bulk. This was the cheapest option. Most of the evidence of weeds will start to disappear now the colder weather has come and weedkiller will no longer be effective until the growing season starts in the spring but I would concentrate on removing as much as you can while you can see it. In the spring you need to get on top of it as fast as possible, get the bark spread on and then jump on the upstarts with well aimed weedkiller as soon as they show. Once you have the bark down we found it not effective to dig weeds out as it renders the bark ineffective if you mix it up with the soil. It becomes just a soil conditioner instead of a weed suppressant.
After DH was injured at the beginning of the year we have had to concentrate on the most labour saving methods we could find. Bark is not the most suitable for every border but the one we used it on is mainly shrubs and trees with bulbs and lily of the valley and we had perennials planted through it afterwards and a huge swathe of mixed antirrhinums - all of which has been very successful. We are very fortunate to have a very good friend who is a professional gardener and who charges us mates' rates or we would have disappeared behind the weeds by now!