Snake bites are part of owning snakes. I never thought of the shirt idea but it just might work. Most snakes when they are getting ready for a shed will tend to be more defensive than normal and can bite. While their bites are generally scratches on our skin they can startle us a great deal when they strike.
One thing you need to understand is the fact that your snake NEEDS to be handled daily otherwise they will not be accustomed to being handled. Keep in mind not to handle them for 2 - 3 days after feeding or you could have a smelly undesired effect. Also once their eyes have started to glaze postphone handling sessions until the shed is complete.
Another thing, wash your hands before you handle your snake. If your snake is biting you you might want to invest in a pair of work gloves and handle your snake wearing those until the bites stop. Each handling session should be as long as you possible, especially as the snake starts to bite less and less frequent. If you leave a hostile snake alone they will only get worse, believe me. It's not too hard to watch tv or surf the net holding a snake as I am doing with my biggest right now.
Hope this helps.