My runner beans are producing lots of flowers which are attracting my
friends the Bees. However no beans, just little a stump where the
flower used to be.

You need to attract more bees to pollenate the flowers. If the bees go
through "the back door" to get at the nectar the flowers will drop off.

Try attracting bees to come more often by very occassionally lightly
spraying the flowers with a sugar solution 1 tsp to 0.5 litres in the
evening.

Plus keep them watered.

If the leaves start to go patchy yellow, lightly spray leaves only and earth
at base (bees do not seem to like it) with chemist's shop Epsom salts at the
same concentration.

Plus keep them well watered!

Regards

Ron.