Yes it is fine to take a bath when you have the measles, it can even act as a way to sooth the irritating itch that sometimes comes with the illness.
It is however a very infectious disease, so you will have to be sure that no one comes in contact with the bath water after you have used it. Once you have finished in the bath then you should be sure to wash the tub thoroughly, to prevent any spread of the illness.
The skin infection is similar to the the chicken pox symptoms, so red and itchy spots or flaky skin. Sometimes the spots and rashes can even be painful.
When having your bath, you can sprinkle some oatmeal into the water as well. As strange as this sounds the oatmeal actually adds a very soothing quality to the bath that can ease the itchiness of the skin.
The brand 'Aveeno' also has a similar effect to the oatmeal if you add it to the bath water. If you don't have either of these products then you can add a small amount of baking soda to the water, this can also help.
Be aware when you are getting in and out of the bath that the oatmeal can make the beth very slippery!
I hope this helps and you feel better soon!