Delete all files and directories but certain ones using Bash

You can use find, ignore mysql and temp, and then rm -rf them.

find . ! -iname mysql ! -iname temp -exec rm -rf {} \;

This is usually a job for find. Try the following command (add -rf if you need a recursive delete):

find . -maxdepth 1 \! \( -name mysql -o -name temp \) -exec rm '{}' \;

(That is, find entries in . but not subdirectories that are not [named mysql or named tmp] and call rm on them.)

You may try:

rm -rf !(mysql|init)

Which is POSIX defined:

 Glob patterns can also contain pattern lists. A pattern list is a sequence
of one or more patterns separated by either | or &. ... The following list
describes valid sub-patterns.

...
!(pattern-list):
    Matches any string that does not match the specified pattern-list.
...

Note: Please, take time to test it first! Either create some test folder, or simply echo the parameter substitution, as duly noted by @mnagel:

echo !(mysql|init)

Adding useful information: if the matching is not active, you may to enable/disable it by using:

shopt extglob                   # shows extglob status
shopt -s extglob                # enables extglob
shopt -u extglob                # disables extglob