Hand-washing is the best way to get all the sweat and smells out of your bra, while also making sure your bra stays in good shape. Put them in your sink with cold water and soap, soak for some hours and hang them over to dry.
So, machine washing may not be the ideal way to clean your bras, but it is still fairly acceptable. Just make sure your machine is on the gentle cycle. You will need one of those little net lingerie laundry bags to put your bras in. And try not to wash your bras along with anything too heavy, such as towels.