Bleaching and dyeing hair after perming can be done, but it is not advisable to perform these chemical processes back-to-back or on the same day due to the potential for severe damage to your hair. Perming chemically alters the hair structure by breaking and reforming the disulfide bonds to create curls or waves. This process already puts a lot of stress on the hair.

Here's what you need to consider:

1. Wait and Assess: It's recommended to wait at least a few weeks (some stylists suggest 4-6 weeks) after a perm to allow your hair to recover and regain some strength before undergoing additional chemical treatments like bleaching or dyeing.
2. Damage Risk: Bleaching involves removing natural pigment and can be highly damaging, especially on hair that has already been through a perm. Dyeing can also be drying and potentially weakening. Doing both consecutively increases the risk of breakage, split ends, and overall hair damage.
3. Hair Health: If your hair is already compromised due to the perm or is naturally fine, brittle, or dry, combining perms with bleaching and dyeing could result in irreversible damage.
4. Professional Advice: Consult with a professional hairstylist who can assess your hair's condition and provide expert guidance on the timing and order of these treatments. They might recommend less invasive alternatives such as toners or gentle coloring methods.

The key to maintaining the health of your hair when doing multiple chemical processes is to space them out, use proper conditioning treatments in between, and always listen to your hair's needs. Remember, healthy hair is the foundation for beautiful styles.