In general showering is easier than getting in and out of a bath. Always use a non slip mat in the bath or shower.
Avoid using strongly scented soaps and body washes. There are unperfumed options.
Avoid using bath oils. They make your bath very slippery and make getting in and out of the bath much more difficult.
Circulate air in a steamy bathroom. Open a window / door to circulate the air, or use an extractor fan.
Some people feel more breathless if they have a shower spray on their face. To avoid this lower the shower head if it is on an adjustable rail.
If you are tired after your bath or shower try using a large towelling bath robe to wrap around yourself to get dry and keep warm at the same time. You can go to sit and rest in another warm room. Use your breathing control techniques and wait until you are dry.
If you have difficulty washing and drying your hair, try using a travel size hairdryer which is much lighter. If you have someone who can help ask them, or make an appointment at your hairdresser to choose an easy to manage hairstyle.