It has many years since I last used taking bearings in anger to fix my position and even quite a few since I actually walked a bearing out of necessity rather than for the fun of it - I think the last time was to work out where the exit was when crossing a large field with a hump in the middle.
I have on occasion taken a note of a bearing to find out what some distant feature was called, but that is just for curiiosity rather than navigational necessity.
In my opinion, when walking in most of England and Wales, the most important skill is getting the map the right way up, for which a compass is useful when the features don't make it blindingly obvious - and even then it can be worth a check to stop you situating the appreciation. Other than that, with few exceptions, and excluding very poor visibility, once you are pointing in the right direction, with decent map reading skills, you should be able to work out where you are and where to go by the features in the terrain.
I think the main secret of success is to navigate pretty constantly rather than intermittently. Always be aware of the features around you and their relationshio with the map and have an idea what is coming up next - a bend in the path, the crossing of a fielfd boundary, an ascent, a stream and so on. That way, if you wander off route, the alarm bells will ring sooner and you stand a better chance of sorting yourself out. Moreover, the more you pay attention to the map and its relationship to the land around you, the more you will begin to appreciate the subtle nuances in the map that not only help you when you are out but will also aid the planning of future walks.