Possibly a typo in either your code or when posting; regardless, \x{BC} is 1/4 as a single character, not mu.

Both substitution and transliteration work, as shown in the code below. [I used the /r option for demonstration purposes. You may not need or want this; but, if you do, you'll need Perl v5.14 or later to use it (see "perl5140delta: Non-destructive substitution").]

$ perl -E '
    use strict;
    use warnings;
    use utf8;
    use open OUT => qw{:encoding(UTF-8) :std};
    use Unicode::UCD "charinfo";

    say "\x{B5} = ", charinfo(0xB5)->{name};
    say "\x{BC} = ", charinfo(0xBC)->{name};
    say "\x{3BC} = ", charinfo(0x3BC)->{name};

    my $contents = "\x{B5} \x{BC} \x{3BC}";
    print "Original \$contents:    ";
    say $contents;
    print "Non-desctructive s///: ";
    say $contents =~ s/[\x{B5}\x{3BC}]/u/gr;
    print "Unchanged \$contents:   ";
    say $contents;
    print "Non-desctructive y///: ";
    say $contents =~ y/\x{B5}\x{3BC}/u/r;
    print "Unchanged \$contents:   ";
    say $contents;
'
[download]

Output:

µ = MICRO SIGN
¼ = VULGAR FRACTION ONE QUARTER
μ = GREEK SMALL LETTER MU
Original $contents:    µ ¼ μ
Non-desctructive s///: u ¼ u
Unchanged $contents:   µ ¼ μ
Non-desctructive y///: u ¼ u
Unchanged $contents:   µ ¼ μ

See also the Unicode PDF code charts: "C1 Controls and Latin-1 Supplement" (for x{B5} & \x{BC}); and, "Greek and Coptic" (for \x{3BC}).