Bash- getting rid of duplicate chars from a set in output

Question

Scenario 1: I have a variable where this string is contained:

    output="abdh748mdn78##j*&#"

the special characters belong to a set called specialchars

    specialchars='@#$%&*+-='

All I want for Christmas is to

1) keep one of the specialchar, discard the rest.

2) delete multiple occurrence of that one char from the string, or alternatively- just choose ONE of the special chars and discard the rest.

Scenario 2:

    output="a#bdh#748m#"

    Speicalchar="$char" [where $char is '#' randomly selected from set- look above]

notice there are multiple #'s

Just need to get rid of the duplicate and keep one. Then echo $output

I tried:

    echo $stringout | sed 's/\([@#$%&*+-=]\)\1/\1/g' 

found it on stackx but it doesn't work.

Need to keep it bash (can only use bash utils).