We have previously talked a lot about henna here, be it the real Lawsonia Inermis and some general facts (read here) or the compound colored henna and its risks, as well as my personal experience with "black henna" (Black Henna Review).
Well, if you have read the two articles linked above, you certainly may have realized two things:
1- Henna doesn't wash out easily. It takes a very long time till the hair grows long enough and then you are left with henna only near your hair ends.
2- Compound henna is not 100% natural henna (or it can even be 100% chemical with no henna at all), and it often reacts very badly with chemical dyes.
So, based on these two facts, before you consider dying or bleaching your already hennaed hair, you need to wait at least for some months till the henna kind of washes out.
Natural pure Lawsonia Inermis is safer, but if you used a compound henna like me, you absolutely need to do a patch test first. You can use some of your shedding hair for that.
The reason why compound henna can be very dangerous when it reacts with the chemical hair dye, is that it might contain either PPD or mineral salts. Those react really badly with some of the ingredients in the dye/bleach.
The risks range from a very awful color result (some people's hair turns green or something like that) to a complete damage of the hair.
So please be careful!