If your hair appears undamaged after the bleaching process, you can dye it right away. Generally, a gentle colour toner is added to gradually change the hair's colour rather than shocking it with a harsher dye. It also prevents colour distortion.
The bleaching process may take a toll on your hair. The stripping chemicals can dry and weaken the hair. If this seems to be the case, treat your hair with a deep conditioner. This will restore moisture and protect the hair for the next dye process.
Deciding how soon to dye your bleached hair mostly depends on the hair's condition, both before and after it was bleached. For example, if your hair was already dry or damaged before it was bleached, you'll likely have to wait longer than someone with healthy hair.