There are national bus services to Whitehaven, and these can be considered, if you are on a tight budget. However, they are much slower than rail – travel time from London to Whitehaven for example is almost 9 hours by bus, whereas fastest train time London – Carlisle is 3 hrs. Also, there are NO bus services to St Bees so you must make Whitehaven your destination. 

You will need to get taxi or train to St Bees. Walking to St Bees via the main road is not advised as it is a narrow road and there is no pavement/sidewalk.

Searches for bus journeys from airports seemed even longer, and the routes being suggested on the National Express web site were surprising! Not recommended unless you want a circuitous mystery tour of northern England.