Splice is much more efficient, and the only reason it isn't working here is you're skipping the item after each item you remove. The following works fine:

my @c = (1..20);
for ($i = 0; $i <= $#c; $i++) {
    if ($c[$i] >= 5 && $c[$i] <= 10) {
        splice(@c,$i,1); $i--;
    }
}
print join ' ', @c;
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Outputs:

1 2 3 4 11 12 13 14 15 16 17 18 19 20
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Or for your example:

my @c = ("bob", "bob", "martha", "bob");
for (my $i = 0; $i <= $#c; $i++) {
    if ($c[$i] eq "bob") {
        splice(@c,$i,1); $i--;
    }
}
print join ' ', @c;
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