Bath or a shower?
Which is cheaper?
A great deal depends on the type of shower, the flow rate and how long you run the shower for.
9.5Kw electric shower, for 2 minutes, at 33p per Kwh - around 10.4p, assuming the shower runs flat out for the entire period.
A bath full of really hot gas heated bath water costs around 30 to 40p.
Both are plus cost of the water if you are on a meter.
In winter I tend to make more use of the bath, because it has the effect of warming me up, and reducing the need for heating the house up.