Separate clothes that have tags which say 'hand wash', 'color may wash off' and 'avoid detergent' is because these clothes are most prone to bleed and color others. Wash these clothes separately in a tub or in a separate load of the washing machine.
The secret to preventing bleeding is to do a wise color sorting. Separate the all-whites from all the colored clothes. White easily catches on the lightest of colors and gets ruined. Do not limit sorting to just whites. Make piles of the same colors and wash them together so that even if there is a color bleed, it is of the same color and does not create a disaster.
Fabrics like cotton and wool are not color fast and bleed easily. While washing these fabrics, be very careful. If you are not sure about whether a fabric bleeds or not, test a part of it in a tub of water before washing. If it bleeds, wash it separately. You can also test by pressing a white wet cloth to the fabric and examining for any color bleeding.
There is a way to make your fabrics color fast. Vinegar has the properties of strengthening fabric color. Mix a cup of white vinegar in a quart of water in a tub. Soak the clothes overnight. The colors will set in and the bleeding will be reduced. Commercial dye fixatives are also easily available that fasten fabric color and reduce the color discharge. Just soak your clothes in the dye fixative.
Place a color catch cloth in your washing machine. This cloth will absorb the excess dye and keep it from bleeding into other fabrics. This way your other clothes will remain safe.