If you have a hot water storage cylinder, usually found in the airing cupboard, you should be able to run a bath and have a shower at the same time.
If you have a combi boiler, which heats the water as it is needed and doesn't have a hot water storage cylinder, and you open two taps, the boiler will split the water between them and you will get a reduced flow rate of hot water at both taps.
If you regularly need lots of hot water at the same time, it is worth considering having a system boiler, such as Baxi EcoBlue System and hot water storage cylinder, such as a Baxi Megaflo Eco, to ensure you always have enough hot water. Your installer can survey your home and advise the best boiler to suit your needs.
Find a Baxi installer near you for a free quote to install your new boiler.