I would not use 'date' as a field name, but it may be legal.
The following does work with Postgres, should be okay with Mysql.

UPDATE: The original poster said "my sql", Mysql is just my imagination.

Make a database with a table like so:

create table mileage ( day date, purpose int);
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It is good to try to condense problems like these to the smallest
free standing code that demonstrates the problem. When
you do this you may find the problem in your code. When
doing mixed language developement it is easier to make syntactic
mistakes and more likely that your tools will not report
them well.

#!/usr/bin/perl -w
use strict;
use DBI;

my $dbh = DBI->connect("dbi:Pg:dbname=t", "use", "pw")
        or die "cant connect: $!\n";

my $s = $dbh->prepare(
        "SELECT day, purpose
        FROM mileage
        WHERE day BETWEEN ? and ?
        ORDER BY day"
);

$s->bind_param(1, "1999-01-01", {TYPE=>DBI::SQL_VARCHAR} );
$s->bind_param(2, "1999-12-31", {TYPE=>DBI::SQL_VARCHAR} );


$s->execute;

while ( my @row = $s->fetchrow_array)
{
    print "$row[0], $row[1], \n";
}
$s->finish;
$dbh->disconnect;
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