I know I'm 12 years late but I just had the same problem and it's still not magically solved in recent versions. However, I found another solution that might be interesting for someone like me who stumbles across this and has the same problem!

Similar to pg, I tried to insert a 1 or a 0 to a BIT(1) field in a MySQL table via DBI with placeholders. It did not work, same error. But I remembered that I previously had to convert the values from a query on said field that were returned by DBI (i.e. make "perl numbers" from the binary data):

Et voilá, the reverse (pack) worked fine with DBI, I didn't even needed to use bind_params()!

use strict;
use warnings;
use DBI;

my $dbh = DBI->connect("DBI:mysql:database=Foo", "user", "password", {
+mysql_enable_utf8 => 1, RaiseError => 1, AutoCommit => 0}) or die "Ca
+nnot connect to database: $DBI::errstr";

my $statement = "insert into testtable(bitfield) values(?);";
my $insertnumber = pack("b",0);

my $sth = $dbh->prepare($statement);
$sth->execute($insertnumber);
$dbh->commit;
$dbh->disconnect;
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